What does Vector mean in nodes input and output in Blender?
Well as the name implies, it's a vector, a 3 dimensional vector with 3 components
z. It's different from, for example, the scalar (grey) socket which is a scalar value or the yellow socket which is a color value (consisting actually of 4 components R, G, B, and A or 3 if we have no Alpha).
You can see the vector socket as 3 grey sockets combined and the color socket as 4 grey sockets combined (3 without Alpha).
You can use the
Converter>Combine RGBA to convert from scalar value to vector, RGB or RGBA respectively.
You can also get each individual components of a vector, RGB or RGBA color by using their
Converter>Separate counterparts :
The rule of thumb is that you should (almost) never plug two sockets of different colors to each other unless you know exactly what you are doing.