Its easy enough to send somebody a YouTube link, but when a video contains a bunch of crap at the start or you want to skip straight to the good part, its handy to know how to skip straight to the bits that are interesting.
Take for example this link:
If I wanted to show the fun parts of the video that start at 0:51, I'd have to tell the person "Hey, watch this and skip to 0:51 because theres a bunch of stupid kids at the beginning that nobody cares about".
They'd have to open the video, wait for it to load and then drag the cursor to the given time. That's annoying.
Instead, we can just give them the slightly modified link that'll skip straight to the time given. We add an anchor called "#at=51" at the end of the url so now it should look like:
Now the link given will skip straight to the 51st second of the video.
If the time you're skipping to is over a minute, then you'll have to convert the time to the number of seconds.
For example, skipping to 2m30s takes converts into 150 seconds. The link is now:
Another great example would be this video ;)