When we let a magnet fall freely inside a vertical copper pipe it slows down. Copper is not magnetic in nature then how does it exert force on the magnet?
If you have the tools to experiment this then you should try it. Bring a magnet near a closed loop of wire and as you move the magnet you'll see that current is induced in the wire! (check it with a galvanometer)
The number of magnetic field lines that pass through the wire is changing when you move it and that induces electric current in the wire. The direction of the current can be in two directions but it will always be in the direction which will oppose the change in number of field lines that pass through it.
We can prove this by contradiction, let's assume that the change in number of magnetic field lines that pass through a wire loop induces a current that doesn't oppose the change.
We'll conduct an experiment to prove this wrong. Take a copper pipe and hold it horizontally (parallel to the surface of flat earth). Now remove the earth from below or just ignore the earth's gravity. Take the magnet and push it inside the copper pipe.
If the Law of Conservation of energy holds true then our initial assumption was wrong! We've just created a free energy device in our imaginary world.
According to our assumption the magnet should not slow down because the induced current is in the direction that does not oppose the motion of the magnet. Now that means it is in the direction that will accelerate the magnet. We've put a finite amount of energy in an isolated system, then how is the pipe accelerating the magnet? Where is this extra energy coming from?
This breaks the Law of Conservation of energy and that is the reason why the copper pipe will always oppose the motion of the magnet. The pipe wants the number of field lines that pass through it to not change and so the electric current which induces a magnetic field opposes the motion of the magnet.
Metal drums are attached to the car wheels and it is covered with strong electromagnets, when we pass current through the electromagnets a very strong magnetic field is generated and the number of magnetic field lines passing through the drum changes because the car is in motion. The metal drum wants the magnetic flux (number of magnetic field lines that pass through a cross section) to remain same and so it opposes the motion of the electromagnet but the electromagnets are fixed and so the metal drums slow themselves which in turn brings the car to halt.
We call this induced current as Eddy Currents