It was cheap, durable, and ubiquitous. It had sound and graphics capabilities far in excess of any of it's contemporaries (at that price point, at least). It was also quite open and came with a manual with lots of neat technical detail.
It also had quite a nice keyboard, even by today's standards.
This, this and this. Where & when I grew up - rural Norway in the eighties - just about everybody had one, ensuring that no matter what you wanted to do, someone nearby were into the same thing; magazines with code listings, books and -ahem- evaluation copies of software were all over the place; as were peripherals - this basically meant that any latecomer to personal computing chose the C64 as it was everywhere, creating a huge positive feedback loop if you got into the C64.
Poor kids next door - their parents got a good (for the seller!) price on a Dragon 32; the nearest Dragon 32 to theirs probably was in Aberdeenshire or thereabouts...
Or MSX. Don't know in Norway, but in Sweden the Sinclair Spectrum was also very popular, but not as popular as the C64. Rough partition - affluent kids, C64, less affluent kids but still with geeky or generous parents, Spectrum. The poor suckers (like me) Spectravideo MSX :-D
It also had quite a nice keyboard, even by today's standards.
They really don't make them like that any more.