Easy! Opera mini is so fast compared to all fully-fledged browsers. The thing is that it compresses all sorts of data including pictures, audio, videos, and yes, even adverts! Another great feature is that it has built-in ad blocking if you want no ads at all (I keep this off though because it slows Opera Mini down somewhat.)
Another thing that Opera implemented chini ya maji in the current Opera Mini is that they gave it full functionality if you choose to use it. If you set data savings to high as opposed to extreme, Opera Mini performs exactly the same as its big Brother.
Do you know a site called html5test.com? It basically tests how ready your browser is to support the latest website features. If you test Opera and Opera Mini on high data savings, they get the same score (about 502 points.) However, turning data savings to extreme in Opera Mini makes it a lot more docile with a score of about 250. To compare these figures, Google Chrome is the highest scoring browser at 518 points and Firefox scores 486.
FYI, Chrome and Opera are pretty much the same thing because they both use the Chromium open source engine. Chrome scores higher because of better optimization - - they do have more experience with the browser engine which Opera adopted like 3 years ago.