I can easily explain why.
1. He's popular because he writes songs with catchy hooks and has a definitive songwriting style. They usually have unique titles and expression. Like 0 to 100, The Motto, Hotling Bling, Worst Behavior, etc. Songs that have unique titles and repetitive hooks are easy to remember not to mention more appealing. You see a unique name for a song and wonder what it's about.
2. He merged Hip-hop and R&B in a new way. Instead of the faster tempo, 6/8 type time of most hip hop songs before him. 40 or whoever thought of keeping the time, slowing the tempo, adding a special accent to the beat and also creating more spacious beats. With a more avant garde , also atmospheric chords in the back and creepy melodies used catchy(learned from lil Wayne you can tell). So basically musically, they made hip hop more R&B ish.
3. More on the merging of Hip-hop and R&B, Drake took the "blues" out of Rhythm and Blues(R&B) and applied it to his lyrics. Drake was literally the first successful emotional rapper, the singing helps sort of but he's not that great. It's the lyrical content with the mix that enhances that R&B feel. After that everyone started singing, even people that are better singers and rappers like Gambino.
4. Because of his emotional lyrics and reminiscence of R&B, he attracted a huge female fan base. Which is the most important aspect of mainstream success. Female fans are the most supportive, it's just how it is. Think of all the biggest mainstream artists, Taylor Switft, Justin Beiber, Drake, One Direction. They're huge largely in part to their appeal to females and their female audience.
I don't mind him honestly. I do just hate that he is only making music for money though, when at his position he could do extrodinary things for mainstream music. Especially since that's the first music the majority of the public are introduced too in life.