What Are Translations, in Geometry?

Translating a figure means moving it

Translation is just a fancy word for "moving." When we translate a figure in math, we're just moving it from one location to another, without any rotation. Everything about its size, shape, and orientation stay the same.

In the image below, the shape is translated down and to the right, so that the top left corner moves from $(-1.25, 1)$ to $(-0.25, 0)$.