The main quest of Skyrim follows your discovery of being the Dragonborn (also called Dovahkiin by the Dragons). This quest will take you all over Skyrim learning about your latent skills and how to stop the Dragons from returning. This main quest is great for getting you started but around halfway through, the difficulty spikes. This is usually a good time to start taking on faction quests so you can beef yourself up a little bit.
If you beat the main quest, you will be able to continue playing afterward to complete any other quests you like and to play around in Skyrim.