Adding to and clarifying metengr's post a bit:
As noted, the "S" prefix indicates an ASME material spec. In most cases these are identical to ASTM, but certainly not all. For example, SA-106 was not harmonized with A-106 for several years when ASTM made some changes which the ASME found unpalatable.
A indicates that it is a ferrous material. Material specifications for SA materials can be found in Section II Part A. If you had a "SB" material it would indicate that it is the ASME version of a non-ferrous material. Material specifications for SB materials can be found in Section II Part B.
The specification number, in this example "516" is just an identifier. As far as I know it has no technical significance. Perhaps chronological?
The grade identifier can be many different things. For example, SA-285-C the "C" in and of itself is meaningless; one has to read the SA-285 specification to understand what the specific requirements for grade C are. In the case of the 516 series, the grade number correlates to the specified minimum ultimate tensile stress in ksi. So for SA516-70, the specified minimum UTS is 70 ksi while SA516-60 would have a specified minimum UTS of 60 ksi.
