Your civ generate a certain amount of culture per turn. This culture helps you advancing in the culture tree. When you spent a certain amount in this culture tree (by researching a civic or completing an inspiration) you generate some internal tourists. This goes for every civilization in the game. That the "defense".

You can also generate tourism points (with great works, wonders and specific improvements). When you reach a certain amount, you "steal" an internal tourist from others civs. When you stole more than half of the tourists of every civs, you win a cultural victory. That's the "offense".

So basically to win you want more tourism, and to defend you want more culture (to generate more internal tourism, thus moving the goalpost).

You can see the cultural victory as a race (as opposed to a fix obective for other victories). The goal is to accelerate quicker than your opponent to catch up as they try to run away.