Exclusive rights means you are transferring them full ownership of the beat. They own the copyrights and may do what they please with the beat because it is now theirs. You cannot reuse or resell the beat without written consent.

There are advantages and disadvantages to selling exclusive rights to the beat. One main advantage is you can charge a significantly larger amount for exclusive rights. Prices vary drastically from producer to producer but just make sure you don't go selling your beats exclusively for like $200 because you are losing out on serious cash. The biggest disadvantage is that you will never get to use the beat again because legally it's not yours.

Leasing is selling only limited rights to your beats. The rights are whatever you specify in the contract (e.g. you could say that they are only allowed to sell 5000 copies of the song). I generally give them rights to use the beat, but I still own the beat and can resell it as many times as I wish. This is great because you can sell the beat as many times as you want and you still own full rights to the beats. Instead of making $2,500 one time on 1 beat, I'd rather lease it 100 times for $40.