What's most important: Igneous rocks are split into categories based on texture, and minerals. The texture indicates the cooling rate of the rock, which gives insight into formation history of the rock. The mineral composition indicates the composition of the source magma, which gives insight into the formation history of the rock.

Rocks are made up of minerals. The rules for what is or is not a rock are much broader that the strict rules of minerals. For igneous rocks, the only requirement is that it is material which has formed from cooled lava or magma. To split up such a broad category into more understandable sections geologists divide the rocks by 1) What minerals they have (mineral composition), and 2) The size of the minerals they have (texture).

Glass: This is just like is sounds, the rock will look like a piece of glass, or a piece of glass crumbled and then glued back together. The surface should look like a glass, although the color is likely to be dark. This results when rocks are cooled so fast that the atoms do not have enough time to form crystals before it’s frozen.
Aphanitic: This means “Cannot See” in Latin. This is a geology class, so what they “cannot see” are the minerals inside the rock. This rocks are formed when the magma cools slow enough to
Porphyritic: A porphyritic rock has a mixture of crystals, some so small you cannot see them, and other quite large that you can see them. This results when a source magma cools at two different rates, most likely slowly at first, and then quickly later.
Phaneritic: This means “I can see them”, and its talking about the minerals that can be seen. What it more specifically means is that the minerals formed crystals which are large enough that a human eye does not need help to see them. This is formed by magmas that mostly likely cooled underground, and cooled slowly.
Pyroclastic: This Latin word means “Fire rock fragments” and is a special type of rock that is made of igneous rocks, that were created as small crumbs that were then squished together.
Pegmatic (pegmatite): This is a special type of rock that cooled very very slowly, so slowly that it formed very large crystals. If the crystals in a rock are larger than a quarter, it is a pegmatite.

This is why learning all those minerals was so important! Geologists and geology students alike will look at a rock and figure out exactly which minerals are inside of it, and record those minerals. In addition to "What" minerals are inside a rock, "How much" is also an important question. For estimating how much of a mineral is inside of a rock, numerically inclined modern geologists will use image processing on computers to put a reliable and reproducible number on how much of each mineral there is. In the field geologists often rely upon charts which show visually what 2% of a mineral looks like in a rock.

With so many minerals out there, geologists need an easier way to group the mineral compositions into larger "bins". In this case they use 4 classes which successively high silica composition: Ultramafic, Mafic, Intermediate, Felsic.

Obsidian
Pumice
Tuff (Rhyolite Tuff, Volcanic Tuff)
Rhyolite
Vesicular Basalt (Scoria)
Basalt
Andesite
Diorite
Gabbro
Granite
Granite Pegmatite