What is Race?

When i first heard the question what is race my first though was:  Race is a social construct used to differentiate between people based on skin pigmentation. My next thought was its importance: Race began as an arbitrary entity that has been reified over time, thus made important. As my peers and I stated what we thought race meant to us i began to look at the things scattered on the board and thought : Race can be synonymous with stereotyping.  Our professor  later posed the question Is Race Important?  We came to the consensus that it is but it shouldn't be...... i readily scribbled in my notebook " If race matters then why have people fought so hard for it not to matter?"........