You only see the light that enters your eye!
But it doesn't matter that your eye is smaller or larger than the thing you are looking at.
Hold your hand up in front of your face at arms length. There is some light that reflects of the top of your hand into your eye, and some light from the middle and some from the bottom. It all comes into your eye from different directions and is then focused into an image on the back of your eye.
The "magic" is how a lens (or a curved mirror) can focus light that is coming from different directions into an image. But, of course, it is not really magic. Instead, it is just how light works.
It's the same with a galaxy. If you look at a galaxy there would be some light that comes from the top part, some from the middle and some from the lower part. It gets focused to an image. Galaxies are very faint, so a telescope will gather more light and allow you to magnify the image and make it appear larger.
But there is no greater mystery in why we can see the whole of a galaxy than why we can see the whole of a hand when it is in front of our eyes. We can see the whole as an image because that is what lenses do.