How do bitcoin adresses get into the Bitcoin system when they're created offline? I am new to Bitcoin, and I am still trying to understand the working of bitaddress.org but get stuck a long the way.

On bitadress.org I can take the site offline and create a public and private key by moving my mouse.     

Once my keys are generated I can send bitcoins to the public key.
But as the site is offline how do my keys get into the bitcoin system?
Addresses are not made known to the Bitcoin network when they are created. An address only gets "into the system" when someone sends bitcoins to said address. If you're not the sender of that transaction, the address can be communicated to the sender by any fashion, e.g. by email, postal letter, or coconut laden African swallow. ;)

Thus, after you've created your keys offline, you may tell the prospective sender of the transaction the address in any fashion and to spend the received coins, you may import the private key into whatever wallet software you prefer.