The English word ‘exchange’ is pretty straight forward, but in the Magic world there are some specific rules that govern what happens when things are exchanged. First of all, when an effect instructs you to exchange something, in order for that to happen all things mentioned must be able to be exchanged. For example, when Puca’s Mischief‘s triggered ability goes on the stack you need to choose two targets. Unlike other targeted abilities, if both of these targets are not legal when the ability resolves then nothing will happen as the exchange cannot take place.
When players exchange life totals, players technically lose or gain the appropriate amount of life so their new total is equal to the total that was exchanged with. This can matter as many abilities care when life is gained or lost.
There are a few other somewhat more unusual exchanges possible in Magic involving exchanging cards in different zones or to exchange entire zones. In instances where cards in different zones are exchanged, all cards involved must be owned by one player. If they are not, then the exchange cannot happen. Also, if any of these zone exchanging cards are attached to another object, they become unattached. Finally, if two entire zones are exchanged and one is empty, you will still move cards to different zones.