A copy of FileMaker Pro can be installed on one machine at a time. If you have needs that require you to install on multiple machines you might want to contact our Sales department to discuss multiple licenese and volume licenses.
It is possible to install the same copy on two different machines (eg. a desktop machine and a laptop), but if they are able to see each other on a network you will only be able to use one machine at a time. Hope that makes sense. But if you want to run it on more than one machine at a time in an office environment, and it sounds like you do, then you need multiple licences. Refer to Steve's post.
There is an option that may be workable here. Buy the one copy of FileMaker Pro, create your solution and share it via Instant Web Publishing. It's not as powerful as having three copies of the software, but in some instances it works quite well.