The SGT is a design specification that only applies to 3.x Dungeons and Dragons. It attempts to tell us when a particular class is well above or below it's intended power level. The intended power level of a class is defined in an unlikely place:
“ Challenge Ratings for NPCs: An NPC with a PC class has a Challenge Rating equal to the NPC’s level. ” —Dungeon Master's Guide, page 37
“ A single monster of a specific Challenge Rating when faced by itself has an Encounter Level about equal to its Challenge Rating. ” —Table 3-1, Dungeon Master's Guide, page 49
Since the only difference between an NPC human with nothing but fighter levels and a PC human with nothing but fighter levels is the person playing them, we will go ahead and assume that the statement holds true for PCs as well. So, a PC of level X can be treated as having a CR of X and an EL of X.
Back to the books for some more definitions...
“ Challenge Rating: This shows the average level of a party of adventurers for which one creature would make an encounter of moderate difficulty. Assume a party of four fresh characters (full hit points, full spells, and equipment appropriate to their levels). Given reasonable luck, the party should be able to win the encounter with some damage but no casualties. ” —Monster Manual, page 7
“ In general, if a creature's Challenge Rating is two lower than a given Encounter Level, then two creatures of that kind equal an encounter of that Encounter Level. . . . The progression holds of doubling the number of creatures for each drop of two places in their individual CR, so that four CR 7 creatures are an EL 11 encounter, [etc]. ” —Dungeon Master's Guide, page 48
“ The average adventuring group should be able to handle four challenging encounters [of an Encounter Level equal to the party level] before they run low on spells, hit points, and other resources. ” —Dungeon Master's Guide, page 50
“ Overpowering: The PCs should run. If they don't they will almost certainly lose. The Encounter Level is five or more levels higher than the party level. ” —Dungeon Master's Guide, page 50
We need to do some work with these before we can get to what the SGT represents. If you have a group of four adventures of level X, they are an EL X+4 encounter. They are supposed to get into a total of four EL X encounters before they start running low on abilities and supplies, and when players start running low on abilities and supplies they start dying. But four of EL X encounters are equal to one EL X+4 encounter, which also happens to be the same EL as the party is. So an encounter of the same EL as the party is supposed to push them towards running low on spells, hit points, and other resources. When that happens, people start dying, and they may die before the monsters do. We can't actually go any higher than this (EL X+5) without the party being supposed to die and lose, so this EL+4 point is as close to 50/50 win/loss as we can get in the rules. What we get from this is that an EL X+4 group against an EL X+4 group should result in a 50/50 fight.
We take that and, since it works backwards too, conclude that an EL X vs EL X fight should be 50/50. If you are a PC of level X you should be able to fight an encounter of your EL and, on average, have a 50/50 success rate. This is the basis of the SGT, and it's also an important point in 3.x DnD. Level is supposed to equal CR, but just like there are specializations and roles for monsters to play, so there are for PCs.
The important bit there is the average. You can not do an SGT for a single encounter and learn anything useful from it. Encounters are different and they play to different strengths and weaknesses. So the SGT attempts to represent different styles of encounters so that you get a range of results. You can very easily have "sure win" results in the SGT, just as you can very easily have "sure loss" results. You can also have "likely win/loss" or "toss up" results. You could even make it more detailed if you wanted to, but since it's largely a thought experiment I don't think you gain anything from it. Then you bundle all of your results up, and if you have an approximately 50% win rate, congratulations, you have passed the SGT! Your level is balanced against challenges of your level, as defined in the DMG.
If you don't have an approximately 50% win rate, congratulations, you have failed the SGT! This doesn't actually mean anything horrible or bad. If you're designing your class and wanted a different set of results, you have a list of encounters to review to help guide you with your revisions. If you don't want to revise anything, then this gives you a sense of what balance level you're at. If you have a lower than 50% rate, it just means that you are less likely to deal with the challenges that the DMG says you should be dealing with and should probably have easier challenges. It would not be appropriate for a high powered game, unless you enjoy feeling overshadowed by other players or being dead often because the DM didn't take your balance level into account. If you have a higher than 50% rate it just means the opposite. It's not appropriate for a low powered game, as you will overshadow your fellow players or steamroll all of the opposition.
That's what SGT tells us. Using DMG definitions and monsters at their published CRs it gives you encounters that are supposed to kill you 50% of the time, on average, and sees how you stack up against a varied set of them. It's not a bad thing to be able to hand a hill giant his head every time, as long as it is balanced out in other places with losing yours. Passing the SGT isn't good or bad on it's own, it just means that you can probably use the monsters in the monster manual that are appropriate for your CR and that you play nicely with other classes that pass the SGT. These are nice things, but they are not the only nice things in the game, and they're not even something you should necessarily strive for. There are lots of ways to play the game, this tool just helps you minimize hidden class based balance issues by picking a point and playing your game to it.