"The infinitude of creation is great enough to make a world, or a Milky Way of worlds, look in comparison with it what a flower or an insect does in comparison with the Earth." ~ Immanuel Kant
Galaxies are monstrous collections of stars, plus dust, gas, light matter, dark matter, and gray matter. In a fundamental way galaxies are primarily how the Universe is organized. They contain anywhere from millions to trillions of stars.
Galaxies are extremely large compared to our solar system. They're crazy huge. EXTREME HUGE! Imagine if our whole damn solar system could fit into a single coffee cup, say a grande caramel macchiato with extra whip. So the Sun is in the very center of the cup and Pluto is out on the edge of the lid where coffee tends to spew out and burn the area between your thumb and forefinger. If our solar system were that size, then our galaxy (the Milky Way) would be the size of the entire North American Continent, Mexico and Canada included. You can put a hell of a lot of coffee cups in North America. Actually we do. But this americano analogy is only about the part of our galaxy that glows brightly in the dark. If you include the outer suburbs of our galactic halo, then it's like comparing a coffee cup to the whole freaking Earth.
As late as the 1920's most astronomers thought the Milky Way was the whole entirety of the Universe. Edwin Hubble exploded that idea when he measured the distance to some of the weirdly spiraled objects in the sky and realized that the Milky Way was only one of a cosmic ocean full of "Island Universes," a phrase he borrowed from Immanuel Kant. That description didn't catch on with science geeks who it turns out preferred "galaxies," a word somewhat related to the fact that from Earth it looks like spilled milk from a Greek deli, goat's milk probably.
Hubble classified the various shapes into a system that is known as the "tuning fork." He could have used a spoon or a knife or an egg beater and it would have been just as good because his reasoning was wrong anyway. He thought all galaxies started out shaped like eggs and grew into whirligigs. We now know that both the eggs and whirligigs developed simultaneously over time, did so independently, but we still use Hubble's fork graphic sometimes because he went to all that trouble to draw it. The different types of galaxies need names and these are names so just print it out and put it on your fridge and smile and nod politely.
Elliptical galaxies are sorted by how roundish or squashed out they appear. An E0 galaxy is very round like a cherry and an E7 galaxy is very elliptical like a grape. The higher the number after the "E," the more eccentric and grapey the ellipse.
Galaxies that are frisbee-ish disk shapes with spiraling arms were classified by Hubble simply as "spiral galaxies" because frisbees weren't invented yet. Some galaxies are flat disks with the spiraling shape, but with a bright bar running across the middle. Hubble named these galaxies "barred spiral galaxies" because coming up with clever new names is hard.
Both the barred and non-barred spiral galaxies are more finely sorted by how tightly they are wrapping their arms around the core. Type "a" have arms wound very tightly to the core and proudly display large central bulges. Type "c" have arms wound loosely and have rather small central bulges, not that it matters.
Some galaxies appear to be a weird combination of the elliptical and spiral galaxies> Hubble labeled them S0 on the tuning fork. These are called "lenticular galaxies" which means "lenticular-like" or "resembling something lenticular." The lenticular galaxies have a rather nice comfortable central bulge and a flat disk like the spiral galaxies, but no spiral arms to speak of. They look like a fried egg on toast, but without the toast.
A third class of galaxy is what Hubble called "irregular." Irregular galaxies are difficult to classify as a spiral or as an elliptical, because they are not spiral or elliptical. They can have almost any shape. Many of these probably resulted from two or more galaxies colliding, or by being reorganized by the gravity from a near miss on a cosmic highway. Galaxies that are extremely odd are sometimes just thrown into a classification called "peculiar" because thinking up names for stuff is hard.