I think that, like some have mentioned, Link's power is a simple one, but a powerful one nonetheless. He has willpower and is pure of heart, which can do great things when used in tandem. He merely has the power to follow through with his good intentions when no one else will seem to act. As cheesy as that sounds, that's how it comes across in the games.
Though this would only work for the games which Link actually has the Triforce of Courage. When you think about it, there has been more times that Link never had the Triforce and still completed his quest, used various items/weapons, and simply already had the courage to save Zelda or whoever he was saving.
In the original LoZ, Link never had the ToC, but rather found individual pieces of the Triforce of Wisdom and eventually obtained the Triforce of Power when he defeated Ganon. It wasn't until AFTER his adventures in AoL that he was granted the Triforce of Courage, so he never even used it during the quest. Link also never had any of the Triforce pieces during the three Four Swords games. In the Wind Waker continuity, Link did not have the ToC in PH or ST. Link did not have the Triforce in ALttP, LA, or MM either, but was still able to complete his quest just fine. In fact, I would consider ALttP Link's most difficult quest, being that he had to overcome so many obstacles and Ganon at what was apparently his most powerful. So 10 of the now 15 (including SS and considering both Oracle titles as one), Link never had any piece of the Triforce nor was he shown to use its power.
So what we have left is OoT, WW, TP, and OoX (not including SS because right now we have no idea what will happen in that). In OoT and WW, Link had the ToC for half to a little over half of his entire journey. In TP, I believe he had the ToC the entire time. But of these games mentioned so far, Link never had any more ability than he had before in those games without the ToC. Now in OoX, Link was never known to actually "have" a piece of the Triforce, though he did have the symbol on the back of his left hand and after defeating the final boss of the linked quest, his hand did light up and his hearts filled, so you can make whatever you want to of that. Equally, Ocarina of Time was the only other game where Link's hand lit up and his hearts refilled (just before the battle with Ganondorf).
Conclusively, there has only ever been two times that Link has apparently used the power of the Triforce: Once in OoT, which we know he did possess the ToC in that game at the time, and second in OoX, which is questionable if he actually had the ToC's power within him, but I believe it can be safely assumed that he did take some power from the Triforce at least during that one scene. So I would say that the ToC really does nothing to alter Link's abilities since he had those same abilities without it, but it can refill his health at certain times. Perhaps you could make some kind of "meaningful" explanation out of this and say that it gave him the "courage" to defeat these final bosses by making him completely healthy and ready for it.
