You can download as many times as you like.
You can even install on as many computers as you like.
However, you can only have 2 installations activated/signed in at any time.
What F.McLion says.
It works fairly seemlessly: if you try to sign-in to Adobe CC on a 3rd machine, you don't even have to find one of the first two in order to sign out. On the 3rd machine it will offer the option to sign out all the others, so you can sign in on the 3rd.