The picture above is an example of a translation. A translation is a sliding motion that doesnt change the orientation of the shape it just changes the location. A horizontal translation is when it moves along the x-axis either left or right and a vertical translation is when it moves up or down along the y-axis. An oblique translation is when you add or subtract a number from both the x and y coordinates almost like moving the shape diagonally. The triangle above was translated 6 horizontally and 2 vertically.
The triangle above is an example of a rotation. Rotations is a turning motion, usually about the origin. They can either be rotated clockwise or counterclockwise. Every time they are rotated 90 degrees the numbers swap places and then you add negative or positive signs depending on which quadrant they end up in.
The pentagon above is an example of a reflection across the y-axis. When you reflect an image it is like a mirror image. Most of the time they are reflected across the x or y-axis but they can also be reflecting across a line. By reflecting it changes the orientation of the figure but it doesnt change any side lengths or angles.
The triangle above is an example of a dilation. The dilation makes the shape bigger or smaller depending on what you dilate it by. If you multiply the x and y by the same number then the shape will stay the same but if you only multiply by one or the other then the shape will become distorted. The triangle above was dilated by a scale factor of 2.