Stabilizer is a thin sheet of fiber that is used to reinforce sewing, embroidery, or anything that you feel needs to be supported. You can purchase it at JoAnn's or your local fabric store. For machine embroidery, I also use a tear away stabilizer. That means that after you embroider your item you can tear it away from the back, leaving just the stabilizer that has been sewn in with your stitching. You sandwich stabilizer to the wrong side of the item.
Hope that helps. :D