Communication with a satellite requires you to focus a narrow Radio Frequency (RF) beam at the satellite. Conventionally this is done with the use of a parabolic dish.
If you (or the satellite) are moving, then you need to maintain the direction of this narrow beam pointing accurately at the satellite. Standard Comms-on-the-Move systems use a mechanical motorised gimbal to keep the parabolic dish pointed at the satellite no matter how or where you move - as shown in the image here.
Phased Arrays work by creating this pointing, or beam-steering, from an array of tiny fixed antennas.
By electronically changing the relative phase for the signal that each element transmits, the (constructive & destructive) combination of all of these small signals creates a larger focused beam in a particular direction.
Because this process is fully electronic, the resulting beam direction can be controlled and directed instantaneously in any direction. It can therefore track the movement of any satellite in the sky, no matter how or where you move, without the need for any mechanical moving parts.
The principal and application of Phased Arrays have been around for decades and is well understood. The challenge has been to miniaturise the technology and improve the performance while reducing the manufacturing cost to an economical price point.