A lot of different things contribute to it. Assuming I'm reading the file right (provincial_conversion_events), it looks like:
On the province level, the biggest factors that will lead to conversion are if
the province is heretical, pagan, the capital, or of the same culture (as the ruler, I assume).
For building improvements, things like travel-type connections will speed it up. Roads, harbors, shipyards, etc. Also, obvious religious buildings will speed it up. The various churches, templar house, monastary, school, and grand palace all speed it up. The bad buildings (thieves guild, etc) and the university slow it down.
Some techs in the province speed it up -- inquisition, extravagant decoration, bible translations specifically. Critical thinking and vernacular literature slow it down.
The power of the population groups affect it. A bonus kicks in if the clergy have power at 35%, with the biggest bonus at 55%. A penalty takes effect if they are at 25% or below. A penalty also takes effect if the peasants have 55+% power or if the burghers have 45+% power.
The ruler you have or put in charge of the province also affects it a good deal. All the pious type traits speed it up (merciful, just, chaste, etc), though especially being zealous or a crusader. Being from one of the religious backgrounds speed it up (detached priest, martial cleric, scholarly theologian, mastermind theologian). Naturally, the sinful traits slow it down, though especially being excommunicated and sceptical. It also looks as if having a good stewardship score will speed it up.
Realm stability affects conversion as well. Positive stability helps, zero or negative stability hurts.
Finally, it also looks like the knight orders (teutons, templars, or hospitalers) also get a bonus to convert in their lands.