The 7.92 sS (Schwerer Spitzgeschoss) heavy bullet cartridge with a nominally 12.8g / 197gn JMJBT bullet was adopted as the standard German military round prior to WW2. It had been developed late in WW1 to give machineguns firing on fixed bearings en masse enhanced range and striking power. (This was a feature of both sides' use of MGs in the later stages of trench warfare on the western front - MGs were given additional roles with groupings of up to battalion size being used as rifle calibre mini-artillery saturating the other side's support trenches and forward supply dumps with shoots at ranges of up to 4,000-5,000 yards in indirect fire missions during the night when all sides moved units and supplies around, did maintenance work etc.)
For logistics reasons, the Germans decided to standardise on this round in 1934 at the time the country started to rebuild its armed forces and reequip them with new or enhanced weaponry. The front end of the rifle chamber was altered with a new long tapering leade and revised throat to allow this very high pressure round to be fired safely in this type of weapon. The downside was that alongside the length and weight reduction of the rifle involved in adopting the KAR98k at the same time, recoil and muzzle blast were very heavy indeed - and remain so with most surplus ammunition as found today.
If you read General Julian Hatcher's Notebook the US Army did exactly the same thing between the wars but then had a change of heart and rowed back. When the US entered the European war in 1917, she was so short of MGs that the US Expeditionary Force had to borrow French and British weapons and be supplied by her allies with parts and ammunition. Once .30-06 Colt manufactured M1895 'potato diggers' started to be manufactured in quantity and supplied to US units, the units reverted to their own equipment firing the standard early 20th century version of the .30-06 with a 150gn flat-base FMJ bullet at a nominal 2,700 fps MV. According to the US Army issued Ingles ballistic tables, this had a maximum range of around 5,000 yards, similar to that of the British and French .303 and 8mm rounds, but American machinegunners soon found that these were optimistic. Hatcher did work post war on Daytona Beach Florida firing an MG along the high water line with observers stationed downrange and found that its actual maximum range was only 3,500 yards or so.
Given the tactical doctrines that had evolved during WW1, the US Army was severely disadvantaged by the .30-06 ballistics in MG use, so a great deal of work was undertaken to develop a new heavy bullet L-R version of the cartridge, starting with acquiring 174gn .308 FMJBT bullets from Swiss ordnance, Col Rubin (of Schmidt Rubin fame) being one of the most innovative of cartridge and bullet designers and taking the design from there. The result was the 1920s M1 cartridge, a hot 173gn FMJBT number. As Germany was later to do, it was decided that for logistical reasons the M1 would become the standard US ball cartridge for use in both MGs and rifles. But first tens of millions of leftover 150gn 30-06 rounds in store had to be used up and this took until the mid to late 1930s. By that time, interest in L-R MG fire had waned, the WW1 generation of infantry regimental and field officers had moved on and their senior officers often retired, so few could even remember why the M1 had been designed.
Moreover, when the M1 was finally issued to infantry units for training and familiarisation, it proved to be very unpopular with the troops thanks to (surprise, surprise) excessive muzzle blast and recoil. Then National Guard units pointed out that the round's maximum potential range exceeded that of danger areas on their firing ranges creating a possible safety hazard. So, the ball cartridge M2 with a 152gn flat-base FMJ at 2,800 fps nominal was developed in the late 30s initially for Guard use and units were expected to revert to the M1 in the event of a shooting war. But before the USA entered WW2, there was a change of heart and the M1 was quietly dropped and the M2 standardised for all 30-06 weapons. If the machinegunners needed extra range, they fired heavy bullet AP ammunition.
Most major western military powers went down the high-pressure heavy bullet path in this era, Britain having the heavy bullet Mk9z and Finland developing the famous D series of rebated boat-tails for L-R MG use developments of which survive today as 30 or .310-calibre match bullets. Germany and the US were in a minority though in making their machinegun cartridge a 'universal round', and as noted, the US never really implemented the concept. Many European countries that used the 7.92 and had developed their own versions of short '98 Mauser service rifles in 7.92 or bought them from Nazi Germany pre '39 also adopted sS type cartridges.
The upsides were that the sS was a far superior MG loading and that it also made the cartridge more useful in non-infantry roles. The British RAF was severely hindered in the early stages of WW2 by its fighters being equipped with eight Browning 303s, compared to German fighters with the 7.92 and 20mm cannon, the USAAF with .50BMG MGs. British night bombers used the 303 for the entire war for defence and rarely fatally wounded a German night fighter even if they managed hits - unlike US Flying Fortress day bomber gunners with their 50s. The downside was that the 7.92 sS was never a happy choice in an infantry rifle .... but as 90% of the rifle squad's combat effectiveness was derived from the MG34 or later MG42 and their 1,000 rpm fire rates, that was regarded as an acceptable trade. Another downside though is the bulk and weight of these rounds and coupled to the voracious appetite of its MGs on the Ostfront added to Germany's already severe transport and logistical difficulties in supplying her troops in theatre.
It is also worth remarking that German infantry officers had realised that the 7.92X57 was ballistically far too over-specified and created these logistical problems as early as the 1930s. A short-term 'fix' was the development of the 9X19mm calibre SMG and widespread issue of MP38/40 submachineguns to infantry units in early WW2, but the limitations of this cartridge and weapon system were recognised. So serious work started on 'intermediate cartridges' as early as the the 1930s and culminated in the 1942/3 7.92X33 and MP43 / StG44 assault rifles.
So far as the 7.92X57 goes today in recreational target shooting, the facts remain that the cartridge has very little going for it. First, it is an unknown as AFAIK nobody has developed optimised match chambers etc for it, so nobody knows its true potential. Then there is the (poor) bullet situation. The 8mm SMK has so little relevance to today's competition L-R disciplines that Bryan Litz doesn't include it or any 8mm design in his books and invaluable ballistics exercises and reports. Taking Sierra's three G1 velocity-banded values, their average is 0.495. The equivalent for the antediluvian 200gn 0.308 SMK is 0.560 and for the more modern 210gn VLD SMK is 0.637. So, the 200gn 8mm SMK has a very high (ie bad) 'form factor' compared to say a 200-20X Berger Hybrid in .308 given that the 200gn Sierra thirty is an elderly high-drag design and the 210 has been left behind by newer Berger and Hornady designs. Even where allowed into FTR, I would put my money onto an optimised 308 Win loading in ballistics alone - and we know the 308 can produce exceptional precision in this form but have little to work on in the case of the 7.92. QuickLOAD suggests a 7.92X57 run at the CIP limit with a hot high-energy powder (RS60/Re17) might produce another couple of hundred fps in a 32-inch barrel over the 308 with a 200gn Berger, but I suspect 100-150 fps is more attainable. As it is, many 308 FTR shooters who have adopted 200 and 215gn Hybrid loads run them at below maximum performance as the full-house loading recoil reduces scores.
In countries such as Canada, Australia and the UK where there would be no question of 7.92X57mm being allowed into FTR, I'm not even going to comment on this cartridge's lack of competitiveness against 7mm short magnums and the 284, .300 SAUM and WSM in 'Open'. (Note an early successful F-Open cartridge, long ditched in favour of better numbers, was the 7mm Boo-Boo, an 'improved' 8X68 necked-down to 7mm.)