I have a desktop computer and a laptop. I guess if I have one catalog, I can only have it on one computer unless the catalog is in the cloud?
Hopefully you are doing a bit of reading on this.
If you have then you will know that the highlighted statment is essentially a false one by now.
Many photographers, when travelling load their catalog, not necessarily their actual image collection (although this can be done), onto a laptop.
They then travel and shoot, load new images and work on them, keyword them etc, and then export as catalog back to their desktop when they get home.
The benefit is that one can continue to do all library type jobs while away from home, despite the fact that the actual images are safely stored away at home. Even slideshow presentations can be done, from the previews, as long as the previews are the 1:1 variety.
If one needs to bring some images with because they need work in the develop module this can also be done.
However if the motivation for your question is a desire to use Lightroom as a networked application with two users accessing the same catalog simultaneously then this cannot be done.
I have not attempted an exhaustive explanation but hopefully have shared enough information to at least show you some of the possiilities.
Seth Resnicks book enlarges on all sorts of different workflows related to this issue.