t.co is Twitter's URL shortener. It exists to—obviously—shorten URLs for user convenience, but is also an important part of Twitter's infrastructure to prevent the spread of Malware through the network.
The key thing to note is that it's implemented in a way that clients can also display the URL tidily, and unobfuscated. This screenshot is from Twitter itself.
* The link ‘tpm.ly/mpEFB5’ was entered in the original message. This is Talking Points Memo's own URL shortener.
*
http://t.co/ZgMhylk is the actual @href of the link, and users must navigate through this.
* When you hover a link though, we've also expanded the original TPM link to its full form, so users can hover to see exactly where they're going to end up, whether it's a tpm.ly, bit.ly, aw.sm or any other short URL.
The short aesthetic and branding benefit of a service's own shortener is preserved, the full URL is available to users, and the malware filter can do its job. t.co will redirect through tpm.ly, so any analytics they're doing through that service are preserved.
All three of these formats come back through the API in the `entities` section of a status (see:
http://dev.twitter.com/pages/tweet_entities.) See `url`, `display_url`, and `expanded_url`.