Capacitors are a fundamental electronic component and their property of capacitance in Farads (F) are a core part of radio circuitry.
The basic capacitor is a pair of metal plates separated by some form of dielectric insulation.
Electrolytic capacitors are special because they have a lot of capacitance—hundreds or thousands of microfarads (µF)—in a relatively small package.

Most big electrolytic caps are in the radial package where both leads are on one side. The axial package with one lead on each end of the cylinder are sometimes used. See axial vs radial.
Aluminum electrolytic capacitors provide the highest values while remaining relatively inexpensive so are commonly encountered in radio and electronics. This is possible because of wet chemistry; specifically, an electrolyte solution as part of the dielectric layer between metal plates. Aluminum foil is the primary conductive surface and the electrolyte is part of the separating insulator.
Aluminum electrolytic capacitors are frequently used in power supply circuits such as shown below, and are found in most every type of electronics:
OK, so this is wet chemistry but a dry topic. Why are we boring you with all this?
There is a practical point here for those of you who are handy or brave enough to tackle your own electronics repair; hams tend to be a DIY group. Be advised that many functional problems in all sorts of electronics—not just radios—can be attributed to failed aluminum electrolytic capacitors. We hope to encourage you to fix an expensive piece of equipment, not just toss it or pay someone to repair it for you.
Usually an easy fix with just two component leads to un-solder and then re-soldering the replacement. Diagnosis may be obvious as failed parts tend to bulge, leak or rupture. Not always, though, and electrolytics may be bad with no visible distress. Complete diagnosis may require a bit of testing or a special meter to check series equivalent resistance.
Besides batteries, no other electronics component is destined to fail. Even high-quality aluminum electrolytics have an actual life expectancy, on the shelf as well as operational. The electrolyte solution will slowly evaporate over time and performance will degrade until complete failure. Sitting idle for long periods is also bad for electrolytics since they need periodic charging for the insulating layer to stay formed. Any large electrolytic more than 20 years old should be suspect, perhaps even younger ones. Some techs will replace all electrolytics in a unit if it’s old; this shotgun approach is sometimes easier and cheaper than probing with test equipment. Don’t rely on unused ancient stock for spare parts; get fresh capacitors that don’t have one foot in the grave already. “Recapping” is a well-known electronics service term.
Solid electrolytic caps (mainly tantalum) are much more reliable and long-lived but tend to be smaller in value and are far less common, being rather expensive. They also look different than the big cylinders.
By the way, there is some interesting history (late-1990s to early-2000s) on aluminum electrolytic capacitor problems. It’s a good read on industrial espionage gone bad. Apparently a low-cost/quality supplier stole the chemical formula for high-quality electrolytic capacitors but it was incomplete. The missing ingredient was the element that preserves the electrolyte solution so after several months or years these knock-off cheap capacitors would fail, sometimes spectacularly.
These flawed capacitors were used in many name-brand PCs, TVs, monitors, and appliances, so it was a big problem and still rears its ugly head today to a lesser extent (most have failed by now). Read about this phenomenon that earned its own term, “capacitor plague” here and here and here and here and here.
Polarity is an issue with electrolytic caps because of their chemical and physical construction, so observe the + and – terminals carefully.
Special non-polarized electrolytics are occasionally used, mainly for audio frequency coupling.
Large (typically aluminum electrolytic) caps are so important that there are a few more Technician and General class exam questions on the topic:
We’ll leave you with a little bit of humor. Capacitors are occasionally called capacitators in a slangy way, mocking someone for using a seemingly-sophisticated term while being ignorant about the real word. So we have this: