In Geometry, "Translation" simply means Moving ...
... without rotating, resizing or anything else, just moving.
To Translate a shape:
Every point of the shape must move:
To see how this works, try translating different shapes here:
Note: You can translate either by angle-and-distance, or by x-and-y.
Try both to see what happens.
Writing it Down
Sometimes we just want to write down the translation, without showing it on a graph.
Example: to say the shape gets moved 30 Units in the "X" direction, and 40 Units in the "Y" direction, we can write:
(x,y) → (x+30,y+40)
Which says "all the x and y coordinates become x+30 and y+40"