To translate a figure is to simply slide it somewhere else. But in the move, you may not change the figure in any other way. You cannot rotate it, resize it, or flip it over. You may only slide it side to side, up and down.
In the diagram above,the original object is the yellow one on the left. By translating it up and to the right, we get the gray object on the right. This is called the translated "image" of the original. Notice the vertices of the original are labelled A,B etc. By convention, the corresponding vertices of the image are labelled A' B' etc. The small dash after the letter is called a 'prime' so the vertices are pronounced "A prime, B prime" and so on.
In the diagram above, click on "show lines" and note that the segment AA' is congruent and parallel to BB' etc.