If you are going up for a specific part, "sides" are the scene or scenes that all the actors trying out for the part read in the casting session. They are usually provided through an online service a few days prior to your appointment.
If you are just going into a general meeting witth a casting director, then they are offering you to bring in "sides" to read with them. In that case, pick a scene you have worked on in a class. It's best if it's a two person scene, no more than three script pages. You should probably have your part memorized but take in two copies and hold yours to 'glance' at as you do the scene with the reader.
Good Luck.