A finder scope is a low-power (low magnification) telescope that sits on your main telescope. Your main telescope will typically have a narrow field of view, meaning you'll see only a little portion of the sky when you look through it. Your finder scope, with a wider field of view, assists you in pointing your telescope to your desired subject, making it easy to hone in on your target with minimal searching and repositioning.
Center your subject in the finder scope's frame; there are usually crosshairs or a dot so you know when it's central. Now when you look through your telescope's eyepiece, your subject will be centered here too.
Many telescopes include a finder scope with the package but if you need to purchase one separately it's worth knowing there are two main types. One has a straight-through view, and one has a right-angled view. Generally, you'd want a right-angle finder if you have a Newtonian reflector telescope and a straight-through view if you use a refractor or catadioptric due to the location of their eyepieces. Some finder scopes will also be magnified — higher magnification and a narrower field may be desirable if you need pinpoint accuracy.
You'll also come across the terms 'inverted' or 'erect image.' The latter means the finder scope has a correcting prism that flips the image the 'right way up’ (top-to-bottom) and ‘around’ (left-to-right). Some finder scopes don't have a correcting prism, so you see either a back-to-front image or upside down, which might be disorientating and make finding subjects more difficult, especially if you're just starting out.