A common use of a "Demo" in Counter Strike: Source is to capture a hacker (or suspected hacker) and upload to show admins so a ban can be properly placed.
This thread will help you understand how to make a demo and how to find where it is saved to.
Recording A Demo
Step 1:
Join spectator and spectate the suspected hacker.
Step 2:
Go into your console by clicking the "~" key (beside the 1).
After doing that, type this line:
record ThePersonsName
(it is important to have no spaces in the name of the demo)
Example:
Step 3:
After you are finished spectating the suspected hacker you must type STOP in the console. This will stop recording your game.
Example:
NOTE: It is important that each demo has a different name. If recorded with the same name it will overwrite the original demo.
Viewing A Demo
Go into Console and type "Demoui". This will show a box (see below). Press the load button and select the demo you want to view. You are able to speed up or slow down the demo as you like so you can see exactly what is going on, and skip past the parts that don't show anything.
Finding Your Demo
Go into your Cstrike Folder.
Once you are there you can see all your Demo files. They will be labeled as .DEM file.
Click Here to view how to Zip and Upload a Demo.
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Sup all, So the rebuilding has begun, starting with CZ3 first, should be up in the next few days. Please understand that it also means updating our global banning system, stats system, & everything that is tied into all our servers. Valve updated CS:S to OrangeBox, which is basically what TF2 is running on, so everything that we have customized will have to be recompiled again. Its a long & daunting task, but it started a few weeks ago, and I'm working on the banning system and the... 
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