A Variac is a Variable AC volts transformer and is used to control the amount of wall voltage available for use to whatever is plugged into it.
Recall ohms law, V=IR and that Power P = VI. Given the resistence is the same whether or not you use a variac, the lower the voltage supplied the lower the power in watts output. This is why we use them. Less power means less damage when something goes wrong, less damage to the gear and hopefully no damage to you.
For our hobby a variac is mostly used when first inspecting a new piece of equipment. To prevent any nasty surprises new gear is brought up to full mains power very slowly using a variac. You're essentially purposefully limiting the gear under test's power output ability to ensure that you catch any problems that may arise as early and as safely as possible.
If you plan on acquiring gear and powering it on we strongly recommend you plug it into a variac the first time you do. A variac and some kind of current limiting device, like a lightbulb limiter.