A federated address is an address in the format of (firstname.lastname@example.org*bitgo.com). E.g. email@example.com*bitgo.com and makes passing of an address to others far easier than sending a string of characters to another user. BitGo's Stellar addresses are case insensitive just like email addresses. Note that while sending to Stellar addresses that are not bitgo.com, Stellar addresses may be case sensitive. You should always use Stellar addresses in the exact case they are provided to you.
It's important to note that with wallets created in the API, you will need to specify the federated address after the wallet has been created.