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.