-You are awoken by a Ghost, a fragment of the Traveler given sentience and tasked with supporting the Guardians, those capable of wielding the Traveler's light against those that would threaten the solar system (sorta).
-As you travel through Old Russia, you become aware that a Warmind (a powerful AI that coordinated the Solar System's military forces during the Golden Age) survived, and apparently the Hive have a) set up shop on Earth and b) are trying to kill it.
-Looking to understand the new Hive presence on Earth, you go to the moon, where you discover that they're massing an invasion.
-You successfully defuse the upcoming invasion by destroying a Shrine of Oryx, which the Hive use to communicate with their god/king/godking. At some point (memory's a bit cloudy), you also receive a message warning you of a much worse threat brewing on Venus, so you head there to check it out.
-When you reach Venus, you begin clashing with a mysterious race of robots known as the Vex. A mysterious Exo Hunter (who isn't a Guardian, interestingly enough) tells you that these Vex are the absolute worst of the worst out there, and you should really put some effort into stopping them. Apparently they're headquarted in something called the Black Garden, and the Queen of the Reef can help you get there. So you set out for the Reef.
-The Reef is a very strange place. The Queen and her Brother seem to rule there, and they're not terribly fond of outsiders (especially the brother). Still, she thinks it might be useful to have a Guardian owe her a favor, so she tells you that to get into the Black Garden you need to get her the head of a Vex Gate Lord. Having done so, she makes her brother give you the component you need. Unfortunately, it's dead. In the further interest of a) stopping the Vex and b) making absolutely certain both you and the rest of the Guardians would owe her, she makes you aware that you need to go to Mars to recharge the thing. So you do.
-On Mars, you successfully recharge the Gate Lord thingy, though you have to kick the ass of quite a few members of the Cabal (a race of interstellar conquerers using Roman legionare tactics, more or less) to do it. After that, you raid the Black Garden. Once there, you discover something peculiar: the Vex do inded exist in the past, present, and future, and they coordinate across all three. They have begun worshipping an entity they discovered... somewhere, and are conquering reality for it. Apparently, it's vulnerable to something the Guardians are able to bring to the table, so after a quick boss fight it flees. Queue self-congratulatory "this is only the beginning" cutscene.