Final answer:
Tidal heating is the key internal energy source heating Jupiter's largest moons, with the strongest effects seen on Io due to its proximity to Jupiter.
Step-by-step explanation:
The most important internal energy source for the continuous heating of Jupiter's four largest moons is tidal heating. This is due to the substantial gravitational influence Jupiter has on these moons, particularly Io and Europa. Tidal heating occurs as these moons experience variable tidal forces caused by their changing gravitational pull from Jupiter, which leads to gravitational flexing or kneading in their interiors, creating heat. This process is more influential for moons that are closer to the planet, such as Io, which displays violent volcanism as a result.