I'm seeing MANY threads started by people confused about the Swords spawning, so here's some information.
It's a sort of public event, similar to the dregs on pikes event you can get, for DLC preparation (presumably because swords will be equip-able or easy to find). If you're in the right place at the right time you can see three/four Acolytes worshipping a yellow orb, which the Knight of Crota spawns from. He's usually level 3 or 7, and always has a yellow health bar.
Before he spawns you will get warning text that says "the minions of Crota are preparing a ritual", followed by "the blades are invading," which triggers the spawn. Locations I know of on Earth are in the tunnel at the beginning of the Steppes (down the staircase), at the staircase you take when leaving the Steppes to go to the Divide, and at the crashed hive ship thing in the Skywatch, by the old loot cave. They also spawn on Moon.
You can carry the sword for about a minute, but more specifically when you pick it up extra enemies spawn and when they are dead it disappears.
Let me know any information that is missing and I'll add it in.