Electric current moving through a wire creates a magnetic field. Creating that magnetic field is work and takes energy. If it has to do a lot of work, that energy all gets stored in the magnetic field instead of in the load. Then if the electric current stops, the magnetic field collapses and dumps its energy back into the wire. That's impedance. It behaves like the electricity has been delayed and slowed down but it cannot be explained and understood as electricity alone like resistance or capacitance can, it is an electromagnetic phenomenon and can only roughly and imperfectly fit into an electricity-only model. The devil's in the details, and reactance is the devil's name.

The way I remember it from E&M (Phys 102) is that adding an impedance coil to a circuit causes it to resist changes in current flow. This is because the magnetic fields of the coil loops line up in such a way that they basically reinforce one another (due to spatial geometry). More or tighter loops means greater impedance.

It's easiest to think about a DC circuit of course. There, adding an impedance coil gives an effective "inertia" for current changes, i.e. if there's no current flowing at first then there will be a temporary resistance to starting it. Or vice versa if current is already flowing, then the coil will "induce" it to continue for a short time even after the EMF (e.g. battery) source is cut off.

I'm not very familiar with reactance but Wikipedia says it's an element of impedance (alongside reactance as you noted) that arises as opposition to alternating current. As I understand it affects how much current a given voltage can push (i.e. more reactance means a given voltage will yield less current). It's kind of like resistance but instead of converting the energy to heat, it converts it to a phase shift.

I'm far from an expert on any of this and may be way of base from what you're asking so I'm sure someone more knowledgeable could correct me or elaborate.

https://en.wikipedia.org/wiki/Electrical_impedance