The moons and planets formed by accretion of rocky material and volatiles out of the primitive solar nebula. As they finished forming, about 4 Billion Years ago, the surface continued to be bombarde d by the remmanent of planetary material available nearby. This period is called the Period of Late, Heavy Bombardment. From the Period of Late, Heavy Bombardment forward, this is probably what happened to Ganymede:

• it warmed up from inside, which caused the inside to separate
• the interior of Ganymede began to cool off
• there was a late episode of further warming and volcanism, somewhat like case of Mars, which caused the surface to stretch and break, and which created the grooved terrain.