Vector3 represents the coodinates of a point in space, or a translation depending on how you use it. In other frameworks you can also find it named a
Size2D, sometimes simply a tuple of 2 or 3 numbers etc. They all are the same thing, but in Godot it gets its own naming because it is used a lot.
For example, player position in a 2D game will be stored in a Vector2 (x, y). In 3D there are 3 dimensions (x, y, z) so it would be a Vector3.
You can add and subtract vectors together. For example, moving a character requires to add a value to its X and Y coordinates:
# Moves 10 pixels to the right and 5 pixels up
position = position + Vector2(10, -5)
There is a whole field of mathematics dedicated to vectors (part of linear algebra) which is very useful to know in game developement.
You should (must!) read the documentation linked by hungrymonkey because it explains more about it ;)