Similar standalone Web services have offered workarounds for such a feature, however YouTube has gone above and beyond by integrating this into the comments section of each video. Anytime a user writes in a time in their comment, YouTube's system will parse it over and create one of these deep links. For example if you say "The explosion in 2:10 blew my mind" the 2:10 becomes a link to that specific part of the video.
So far this only works on direct video URLs and not embedded clips. The time you want the video to start must be appended by hand with #t=_m_s at the end. You have control over the minutes and seconds, which are what go where the underscores are.
To show you how this works, here's a quick demo:
Deep linking in YouTube from Josh Lowensohn on Vimeo.