The Toga (トーガ) are a mysterious organization that is rarely seen in Glie. They are the only of only two entities allowed beyond the walls, the other being the crows. When they arrive in town with goods to trade, many of Glie's citizens will set up a temporary marketplace in the Great Gate Square, which makes their arrival an exciting and active event.
No one is allowed to interact with the Toga in any way, with the sole exception of the Haibane Renmei's current communicator, who mediates all trade they do with the town.
What else they do is a mystery, but they clearly have other duties outside of trading, as they can also be seen meeting with the communicator in the Western Woods later in the series, after which they silently rescue Rakka from a well.
Upon Rakka mentioning Kuu's Day of Flight, the Toga noticeably react, but say nothing. This, coupled with the Communicator's description of failed Haibane, tends to suggest that the Toga are deeply connected to the Haibane somehow, perhaps even having been former Haibane themselves, who failed to take flight and lost their wings and halos.