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1.
1. The act of trying to read someone else's texts discreetly by casually glancing over their shoulder.

2. Stealing one's phone and going through their message inbox when the owner of the phone isn't there, usually in the bathroom.
1. I found out Sarah and Dave are fighting again when I was text sniping Dave while we were watching a movie.

2. I knew there was something going on between Bob and my sister. I sniped her texts while she was sleeping and there must have been 40 messages from him.
by Eli December 29, 2007
 
2.
The act of noticing someone who you know in a crowd or some other public situation and sending them a text from an unknown position referring to something which they are doing at the time e.g. "Reading by the lakeside, how very avant garde" this simulates the 'shot out of nowhere' effect of a sniper.
<Maria is having coffee>
Scott: (unseen by Maria) <observes Maria from a distance and sends a text> "ooh two sugars, bit of a sweet tooth aren't you?"

Maria: <checks phone and begins looking around aimlessly> replies "where are you?"

Scott: "I'm text sniping, so you have to guess"
by CHC-RPK March 08, 2011