If you want something that's as intuitive as the hydraulic analogy is for DC, you're out of luck. We try to come up with those, but we always wind up saying, "consider this weird, Rube Goldberg gizmo that nobody's ever seen before ..."
But, here's something you can try at home. Take a big heavy melon, slather it in bacon grease, and push it back and forth across the counter top. If you reverse direction rapidly, you'll see that the melon never goes very fast, and it doesn't move very far. If you reverse direction more slowly, and use the same force to move the melon, you'll see that it moves faster and goes farther.
This works best if you live alone, or the other people in your house are away for a few days. It works absolutely best at somebody else's house.
Anyway, the mass of the melon is analogous to inductance. The force you use to push it around is analogous to voltage, and its velocity is analogous to current. In fact, the equations that we'd use to describe the current through an inductor, in terms of the applied voltage, are exactly the same as those we'd use to describe the velocity of the greasy melon, in terms of the applied force. The ratio of the average force to the melon's average velocity is analogous to reactance, the ratio of an inductor's average current to its average current. Reactance is measured in ohms, just like resistance. It varies with frequency - directly for inductors, and inversely for capacitors. And, of course, "average" here means root-mean-squared, or something like it.
It seems that it would be fun to play with notions of capacitance, too, but capacitance doesn't have a familiar analog like mass. It models as a "spring constant" - a number that describes how stiff a spring is. Without bacon grease, where's the sport?
If you really want to understand reactive components and their action in a circuit, you probably have your work cut out for you. As others have noted, reactive components are modeled as imaginary numbers - something like resistances multiplied by the square root of -1. My guess is that they don't teach much of that in the biology department. Those calculations are weird, and it's a lot of material to wade through to develop a usable set of tools. It doesn't take a geek or genius to master those calculations, but you do have to be motivated to do it.
If you want more detail, check the Wikipedia articles on "reactance" and "hydraulic analogy." The latter article does a fairly good job of explaining why analogies break down in describing these phenomena.
