Difference between units and dimensions Though this question may seem related to Physics, I think that at the very root this is a mathematical question and so I have posted this on math.stackexchange. 
Background: Initially I thought that the terms-unit and dimension, refer to the same thing. 
Physical quantities are categorised into fundamental/basic physical quantities and derived physical quantities. A fundamental physical quantity cannot be broken down into simpler physical quantitities, cannot be obtained from other fundamental quantities and all the known physical quantities can be obtained using fundamental quantities. There was a line in my book which stated

Mass, length, time, thermodynamic temperature, electric current, amount of substance, luminous intensity are the seven fundamental quantities and are often called the seven dimensions of the world. Thus the dimension of mass is [M], that of length is [L] and so on. The dimensions of a derived physical quantity are the powers to which the units of the fundamental physical quantities have to be raised in order to represent that derived physical quantity completely.

This is very confusing and I am finding it difficult to understand the difference between the two terms-dimension and unit.
Question: What exactly is the difference between the meaning of the terms unit and dimension?

It's a subtle difference, indeed. I can't really find a good definition of it, other than what @skyking said ("a unit incorporates a property of scale while dimension doesn't"), but here's something that could help you understand better. What looks right to you?


*

*A) My height is a length;

*B) My height is meters. 


Which one?


*

*A) Speed is distance over time;

*B) Speed is inches over seconds. 


A talks about dimensions, B talks about units. It is correct to say that speed is expressed in (or measured in) inches per seconds, but not that it is inches over seconds or inches per seconds. 
(Plus, inches are not SI :) )
