State Lenz's law and hence describe and explain what happens to a magnet travelling through a metal tube

Lenz's law states that the direction of current due to emf induced by a changing magnetic flux is always such that it opposes the change that induced it.

When a magnet travels through a copper tube this induces an emf and current in the tube, this in turn produces a magnetic field which opposes the direction of motion of the magnet. This means the magnet decelerates through the tube.