Geosynchronous describes a certain type of movement by something orbiting Earth, such as a satellite. A geosynchronous orbit is one that moves around Earth at the same speed Earth rotates.
Earth makes one complete rotation approximately every 24 hours (specifically, 23 hours, 56 minutes, 4.1 seconds). Something that's geosynchronous circles Earth once in that same amount of time. A geosynchronous orbit brings a satellite back to the same place in the sky, at the same time, day after day, because its movement is deliberately synchronized with the Earth's rotation. Geosynchronous is from the Greek geo-, "Earth," and synkhronos, "happening at the same time."