Camera sensors come in different sizes; not just different megapixel ratings, but different physical sizes. And, very roughly, the bigger a sensor is physically, the better the image quality. There are lots of other variables to take into account, and we’ll come on to those shortly.
However, the bottom line is that if you’re chasing the best possible image quality, a bigger sensor is better than a smaller one. What is full frame, and what are the alternatives? In the DSLR and mirrorless camera market, there are two main physical sensor sizes. Full frame is the largest, and corresponds to the 36mm x 24mm size of 35mm film negatives.
But there's a smaller APS-C size, which corresponds to the smaller format APS-C snapshot cameras that were popular towards the end of the film era. These APS-C sensors measure approximately 24mm x 16mm, and you can see the size comparison in this diagram. APS-C sensors are sometimes called "crop sensors", because if you use the same lens on both cameras then the smaller APS-C sensor area means that some of the image is cropped.
But that’s not how things work in the real world. In practice, you wouldn’t use the same focal lengths on both formats. With an APS-C camera you'd use a shorter focal length lens which has been designed for that system, with an equivalent angle of view.
APS-C cameras commonly use lenses designed specifically for the smaller format that save on weight and cost. This is where you get the idea of "equivalent" or "effect.