Authorizing a computer on iTunes, means that computer gets permission to access your apps, books, music, movies and other content. There is a limit and you can authorize only 5 computers, but this doesn’t mean you can’t delete one of them and authorize another one.
How to authorize a computer on iTunes
Step 1: Run iTunes on the computer you want to authorize
Step 2: From the Menu bar, choose Store > Authorize This Computer…
Step 3: Enter you Apple ID and click Authorize.
That’s all, now the computer on which you just did all the steps above is Authorized and linked to your Apple ID.