Io is only slightly further away from Jupiter than our Moon is away from Earth. But since Jupiter has 317 times the mass of Earth, the gravitational pull the little moon Io experiences is roughly 250 times stronger than for our Moon. You can calculate this if you look at the force of gravity between two bodies:
F = G*m*M/r^2
Since the mass M is 317 times larger, and r_Io=421000km is only slightly larger than r_Moon=384000km, you get 317*(384000/421000)^2=263 times stronger gravitational forces on the same mass m.
Io has 1.5% of the mass of Earth, our moon is 1.23%... so Io and the Moon are very similar, especially since they are almost the same size and density, too.
As you can see, Earth's gravity was enough to deform the Moon so that its center of mass has moved towards Earth and it has been tidal locked. On Io, the same effect deposits so much energy that the interior stays molten. It is like as if Jupiter is kneading a giant loaf of lava.
The whole story is a bit more complex than what I told you because Io has an orbital resonance with Ganymede and Europa, which keeps the moon in a non-circular orbit at a constant distance. Without it, the tidal forces would slowly make the orbit circular, resulting in a much lower heat generation: