Maybe it's a silly question, but I don't exactly know what is the purpose of obsoleting wonders?

When you build a wonder, you get the token that is placed on the map and has 1, 2, or 3 culture symbols on it, depending on what era it is from. Each wonder also has comes with a card that has a special power on it. Off the top of my head, one gives you free trade each turn, one lets you build figures (army figure or scout) for free, one protects you from being targeted by culture cards, etc.

When you obsolete a wonder, the player who owns that wonder can no longer use the special ability and gets rid of the card. They still keep the wonder on the map and can generate culture tokens from it. But the main power of the wonder is removed.

The Hanging Gardens (the one that gives you a free figure every turn) can be uber-powerful in the early game, as it means that civ never needs to spend a city action building them. In the hands of the Russians or the Germans in particular, this can be deadly. So obsoleting the wonder can level the playing field a bit, shall we say.

Actually, I should say that any of the wonders, in the right hands, can be quite nasty. So I guess it all depends on how much use people are getting out of that funky ability!

I think what the OP may not be getting is that you obsolete *other player's* wonders, not your own.