A Yggdrasill is a more sophisticated version of the zerg overlord, not the least of which is its ability to exert more control over the zerg than its counterpart (30 compared to 8).
Carpenter's Brood used several to coordinate their final defense against the Zerg Swarm. The Brood was defeated, however.
The Yggdrasill is the basic zerg hero overlord in StarEdit. It appears in StarCraft: Insurrection and Twilight Struggle. In the latter, each cerebrate is attended by an Yggdrasill.
Yggdrasil is the world tree in Norse mythology.