I'm just having a little trouble getting my head around how representation theory works. Say for example we are working with the dihedral group D8. Then the degrees of irreducible representations over C are 1,1,1,1,2. So there are 4 (non-equivalent) irreduible representations of degree 1, and one of degree 2. But what does this mean exactly? Can you use each one separately, or do you need all together to have the full representation? Sorry if what I'm asking is really unclear. I understand why we need to use representations of groups, and I've even found them for a higher order dihedral group. My problem is in understanding why you get several for each group and why some are 1D and some 2D in, say, the case of D8.