The treatment you give yourself after your shaves should be what you find nice and appealing to you. There are several choices, and I'm sure you'll find many that will do just fine. As for the ingredients, here's a couple of the common:
Alcohol - this helps disinfect your face and reduce the chance for infections in the very small cuts and abrasions your knife leaves on your skin. They probably are there after your shave, whether you actually bleed or not. It also works as an astringent. Alcohol does dry your skin out.
Witch hazel: This works as an astringent. It helps close the pores after the warm water and tones the skin.
Certain oils, like tea tree and a number of others are used to aid in disinfecting, reducing bacteria, promoting healing of any minor nicks and cuts, etc.
Oils and butters: help moisturize your skin after the stress that the shaving and all our shaving paraphernalia actually puts on it. (soaps can dry your skin, razor may nick, etc.)
Vitamins, proteins and whatnot are also sometimes added to after shave treatments, to help your skin stay healthy.
Personally, I just use a high alcohol % splash to disinfect, and a shea butter moisturizer to counteract any drying. Works fine for me - ymmv
