In the simple sense refractor telescopes are those that use lenses as their objectives rather than mirrors and were the first type of telescopes, the type you can imagine Galileo using. They were first developed in the early 1600’s in Holland before Galileo made his own version and made it the well known instrument we still use today.
The objective lens (the one at the front of the scope) bends light rays towards a focal point where we can view the image through an eyepiece. The bending of light rays like that is known as refraction, hence the name refracting or refractor telescopes. Modern refractors have lenses which are designed to reduce the aberrations which would otherwise occur and blur the resultant images. They are not perfect however and so some chromatic or spherical aberration is still visible especially on cheaper models.
As refractors gather light with their lenses and as magnification depends on the diameter of those objective lenses, they tend to become large and heavy the more one wants to see! Professional refractors can be quite massive but they do produce excellent views. Small refractors on the other hand are incredibly easy to use and set-up quickly for casual observation. Up to diameters of 90mm (three and a half inches) or so they offer great viewing while also offering easy portability and storage.
Refractors also tend to perform better in city and suburban locations where light pollution can be an issue so if you are likely to do most of your viewing from the city or suburbs a refractor is a good choice in most circumstances. They require little maintenance and offer excellent casual observing, perfect for city rooftops and suburban backyards.