When you save a link with Bitly it comes with a 6-7 random character ending. You can customize the ending of this link to something easier to remember or type. This is sometimes referred to as a vanity URL.
For example, you can take a link like this: http://bit.ly/YpsrII
And customize it to look like this: http://bit.ly/bitly_signup
You can customize a link right after you save it. You'll see a small pencil next to your Bitlink. Click on the pencil to edit the customization for your link. When you are finished, click the 'Save' button below.
To customize a link that you've previously saved go to 'Your Bitlinks'. You'll find the round pencil icon at the top of the page, once clicked into your desired Bitlink. Click on the pencil to customize your link. When you are finished, click the 'Save' button below your customized link.
Remember: you have to create a unique customization that nobody else has used before. Customizations are case sensitive.