There are 10 races to choose from at the beginning of The Elder Scrolls V: Skyrim:
Beyond their physical appearances the main differences you will find between the races are in the Magic and Skill categories. All races start with the "Flames" and "Healing" spells, but some get a third starting spell. Each race also gets a unique "Power" that can be used once a day. Some races also start with "Active Effects" which are traits that you always have as that race e.g. Argonians have Resist Disease, which makes you 50% resistant to disease.
The other main difference is that each race has higher levels in certain Skills. Each character gets a 10 point boost in one skill and 5 point boosts in 5 other skills. While this can be helpful if you know what type of character you want to be, it's not crucial that you know your first time through. You will level up in skills use the most, so if you start off as a Nord, which is more suited for heavy combat to start with, you can use spells often to quickly get your magic levels caught up with your combat levels.
Since you can level up any skills regardless of what race you choose, I would recommend selecting a race that has a "Power" and "Active Effect" that you like, as these cannot be changed throughout the game.