Trace Classes let you define the geometry of a trace so that you can easily re-use that geometry later. For example all of your controlled impedance traces will need to be particular widths. Similarly your power traces may all need to be a certain thickness to prevent a voltage drop.
You can configure trace classes by clicking on the trace width from the Trace flyout.
This brings up the Trace Inspector from where you can edit and add new classes.
When you want to route a trace from a particular class you can open this dialog to select the class. You can also tap the '\' key (backslash) to quickly cycle through all trace classes.