Center There are 6 centers. They each have one face. They determine the color of a side.
Edge There are 12 edges. They each have two faces. On a solved cube each edge will match up with 2 centers. An edge is flipped if it is between the correct centers, but oriented opposite to what it should be. For example, red to white and white to red, instead of red to red and white to white. Getting the 4 edges of one side all in their Home Positions is commonly called getting a Cross.
Corner There are 8 corners. They each have three faces. On a solved cube each corner will match up with 3 centers. A corner is twisted if it is in the correct place, but its 3 faces do not match the side they are on.
Side, Face, Layer There are 6 of them. On a solved cube each side will be a solid color. When solving a cube some methods rely heavily on naming the layers:
U = Upper Layer D = Down Layer F = Front Layer
L = Left Layer R = Right Layer B = Back Layer
Home Position The place any given piece lives when the cube is solved. Being in the Home Position means it is oriented correctly as well as in the right place.
Clockwise In relation to someone looking at the face. R means to turn the Right Layer clockwise;
–R means to turn it counterclockwise. R´ (R prime) is a more common way to indicate –R.
First Layer The first layer worked on. Some methods solve a whole layer first; some solve all but one corner; some solve only the edges; some solve only corners; some use a different approach.
Middle Layer The four edges that are adjacent to the First Layer Corners.
Last Layer The last layer solved. Even methods that solve corners last, have first, middle, and last layers when it comes to the edges. LL = Last Layer.
Move Twist a layer either a quarter or half turn. U is a move of the Upper Layer Clockwise 90˚. R2 is a move of the Right Layer 180˚. A move can be clockwise or counterclockwise.
Corner Piece Series
U R –U –L U –R –U L cycles 3 top corners counterclockwise. The Front Right Corner doesn’t move. Cubes twist clockwise. The Front Left Corner moves diagonally from the front to the back. No edges are affected.
–U –L U R –U L U –R cycles 3 top corners clockwise. The Front Left Corner doesn’t move. Cubes twist counterclockwise. The Front Right Corner moves diagonally from the front to the back. No edges are affected.