Professor wants me to accept his school's offer early
In the US, "hope you can accept the offer quickly" has become a set phrase in graduate admissions letters. You have the right and their explicit permission to wait to accept an offer until the deadline they give (such as the April 15th common US graduate school deadline), and you almost universally will not be penalized in any way for taking that time if you need it (i.e., waiting to hear from other schools, going to visit days to see the place in person, etc).

When I say set phrase, I mean that every offer I received from every graduate school had this term in it, so it is actually part of form letters now for many (most?) places in the US.

What does it mean? Simple - everyone would ideally like to know as soon as possible what your decision is, so they can know who is joining. That's it. They would naturally want to know, so if you have already made your decision they would like to know and have you lock it in rather than exhibit the common behavior or waiting until the day before the deadline to submit your decision.

That's it! So don't worry about, at all. All you need to do is is reply and thank them for their offer, perhaps state your excitement at having received the offer (if you genuinely have that reaction!), and let them know you will let them know of your final decision as soon as you have made it. No need to give excuses or be sorry, that's just how this works. No need to feel pressured into deciding sooner, its a big decision and you have the set deadline for lots of good reasons. Make the decision when you have the responses you need, and if there are visit days feel free to wait to accept the offer until after you have gone and met them (especially true if you have multiple offers you are trying to decide between).

Congratulations on your offer, and good luck in your future career!