Ametal rod is 25.000cm long at 25.0 degrees celsius. when heated to 102.0 degrees celsius, it is 25.054 cm long. what is the coefficient of linear expansion for this metal?

You may deduce what it represents by analyzing the formula you just wrote.
Well, the coefficient of linear expansion as the fractional change in length per degree of temperature change. 

ΔL = c x L(initial) x ΔT 

where c is the coefficient of linear expansion. You can rewrite the equation to give you c. 

c = ΔL / [L(initial) x ΔT] 

Just substitute the variables and the answer will be
c = 0.000028. 

Now, what it represents.It may represent the extent to which the rod expands with temperature when compared to its original length.