The best analogy for inductance in electronics is the mass in mechanics. As you need a force to accelerate certain mass from rest to some speed, you need to apply some voltage to an inductor, in order to make a current flow through it.
As you need some time to accelerate the mass to a certain speed, the current through an inductor needs time to reach it's maximum value.
To make a mass, moving at some speed stop, again, you have to apply a force - this time, opposite to the direction of movement.
Similarly, if you remove the voltage source from an inductor, it will create its own voltage, in order to keep the current flow in the same direction.
Same as a mass moving at some speed has a certain kinetic energy, an inductor with a current flowing through it stores a certain electrical energy.

So let's make an inductor!

what you need to make inductor
First, get a ferromagnetic core and a copper wire. In my case the core has a diameter of 8mm and is 15mm long. The bigger the core diameter - the bigger current and power the inductor can handle. The length of the wire can be calculated by multiplying core diameter first 3.14, than by the number of windings / turns, and then adding, say, 15% - for our project - 8x3.14x60=151 cm, +15%=173 cm.
inductor winding
Start winding. Remember it is not an simple task – make a few turns and fix it with a moment glue. Finish the first layer and again glue it. This will make an even base for the next layer of turns.
inductor winding
Finish the second layer and glue it. Clear the ends of the wire from the insulation. For thin wires, use the flame of a lighter or a small propane torch and a sand paper.
inductor measurement
Check what you have made so far.
For simple projects as a bright LED supply, you would not care about the exact value of the inductor, but for inductors that handle big currents, you have to make sure, that the value of your DIY inductor is within 10% limit of tolerance of the target value.
inductor contacts
Solder the leads of the inductor. Cut offs from resistors or capacitors might be useful.
ready Homemade inductor
Put a thermo shrink tube on the inductor. This way it will be more mechanically durable.
Your Homemade inductor is ready!
This is an example how you can make an inductor yourself. For more sophisticated projects, you have to familiarize yourself with terms like: core saturation, skin effect, leakage inductance, parasitic capacitance.

These recourses will be useful for you, if you want to extend you knowledge about inductors: A well balanced site between theory and practice of inductors, transformers, flyback DC convertors. Online calculator for coil and transformer properties. Gives values for inductance, Bmax, saturation current, and many more. Explanation how inductors work, examples, pictures.
excellentIT(4000)EN version is in English Free SMPS transformer calculation tool made by Vladimir Denisenko.