A race in DDO refers to the ancestry of your character. Did you receive mostly human genes, or dwarf genes.
Every race has some unique aspects: height, strength, agility and a myriad of others. Some races get extra feats, or skills, or increased abilities. Choosing the race you use could be synergistic to the class you plan on using, or make it harder to play the style you want.
There are currently 17 races available, 11 of them standard races, and 6 of them Iconics.
For details about any of the standard races select the race from above.