When I steer left/right in my 2002 Accord, I hear some strange noises. I've uploaded a video, to show what I hear.

Video of what I hear

 

can't distinguish from your video, and don't know how much you know about car troubleshooting.

clicking when you're turning at slow (parking lot) speeds very typically means your CV joints are wearing out - always due to a torn CV (rubber) boot letting the grease escape.
Since can't tell from your video - when car is stationary - give it a slow drive and turn ...

 

The clicking in the video isn't CV axles.

It sounds like it's only happening when you reach close to the furthest point in steering each direction.
If you're not into wrenching on stuff yourself just take it for a front end inspection somewhere, it's probably a bad bushing or linkage causing two components to clunk against each other.
Otherwise put it up on jack stands and wiggle stuff around attached to your steering system, eventually you'll probably find some free play and you can identify the problem from there.