There are various different options.
If you control both computers and would like to use the same user on both computers (e.g., your desktop PC and your laptop), you can log on using the same account and then set application up to sync your library to EndNote’s servers automatically. That way, any changes made on one machine will be synced to the other one the next time you open EndNote.
If you’re more than one user (e.g., you’re collaborating with someone else), you can set up a shared library on your account, which the other person can then open and use. Your library is then the master library, and theirs is a copy. The other person can even set their EndNote to sync to your shared library as well, so that changes they make in their copy will be reflected in your master library.