The Instagram Website briefly explains that Insta came from the childhood memories of cameras claiming to be instant back in the day when we normally had to wait for our film to be developed. Gram comes from the idea that we are sending digital telegrams to each other over the wire. Combine them together for the uniquely perfect “Instagram”.
In a Quora discussion on the topic Kevin Systrom (co-founder) pointed out two other important qualities. The name can be easily understood and spelled out when it is heard, and It embodies the spirit of “right here, right now.”
“It also sounded camera-y.” - Quora Oct. 2010
Kevin Systrom and Mike Krieger built instagram from the ground up in 2010. The app very quickly went to the #1 photo app on both iTunes and now Google Play. Facebook bought Instagram for $1 Billion in April 2012.