Translation
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 angleanddistance, or by xandy.
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:
Which says "all the x and y coordinates become x+30 and y+40"