Does turning on this option on iTunes makes the quality of videos taken on the phone to standard quality as well, or is it just for the videos I watch?
If you buy HD content in iTunes it also downloads a standard resolution copy of the video--you can validate in the filesystem. The HD content in iTunes requires much more space than does a standard def video. This option tells iTunes to copy the standard def video to your device, which does not consume as much device space. This has no bearing on video you take with your phone.
I believe it only affects videos purchased from the iTunes Store. It's been a while since I've bought any video from there, but I remember when purchasing HD content, you get an SD video, too. This option would only copy over the SD video to your phone, if available.
The videos you take with the camera will still be HD.
When "Prefer Standard-definition Videos" is enabled, correct it only copies SD videos. However you don't need this enabled if you have purchased all SD videos from iTunes or recorded DVR to Mac/PC and used a convertor to transfer to iPhone.
Apple sells HD videos in a separate category for those not wanting to purchase 3GB HD movies or 1.5GB HDTV shows (variance in time length).
If you want to understand more about standard definition (SD) and high definition (HD) content I suggest you do a google or wikipedia search for these terms – far better than someone giving a long-winded answer to this here.
As for the second part of your question, this thread does explain very well what selecting the SD option in iTunes does.