In short, Snapchat uses a lot of data because sending and receiving photos and videos requires sending a lot of data from phone to phone, so that the images and video appear correctly.
This is what Snapchat had to say about how much data their app uses:
Because Snapchat uses quite a lot of data, I would seriously recommend you try using Wifi as much as possible as this doesn't use up your data.
"Snapchat images are typically 30-50 kilobytes -- if you have a 1 gigabyte data plan, that would be roughly 20,000 images sent and received per month! A 10-second video snap uses approx. 400 kilobytes of data."