The Trash Hole is an alternate dimension which Raven is able to open a portal to. The Titans regularly use it to dispose of their garbage, hence the name. After the events of "Terra-ized", Terra gets imprisoned there for six months before escaping. She returns there by the end of every episode she has appeared in.
The Trash Hole makes its first appearance in "Terra-ized", during Terra's fight with Raven. In the final moments of their fight, Raven opens up a portal that sucks Terra into an alternate dimension.
In "Be Mine", it is revealed that Terra has been trapped in the alternate dimension for six months, and she finds trash constantly being dumped from above. It's also revealed the place Raven banished Terra is the same place the Titans use to dispose of their garbage, leading it to be termed the "trash hole". Terra has spent all this time plotting her revenge on the Titans, having made statues of them out of trash and crushes them with her rocks. After Cyborg finds out Terra is trapped in the trash hole, he accidentally spills this information to Beast Boy, who resorts to rescuing Terra from the trash hole. After getting Raven to open up a portal, Beast Boy drops a rope down into the hole, and Terra climbs out finally escaping the trash hole.
The Trash Hole reappears at the end of the episode, during Raven and Terra's second fight. Only this time after Terra falls in, Beast Boy jumps in after her, not wanting to be separated from Terra again. While Terra is annoyed at having returned to her place of imprisonment, Beast Boy is happy to finally be with her and loves the chili that drops down.
In "Rocks and Water", during a flashback, it is shown that Beast Boy and Terra spent an unknown amount of time trapped in the Trash Hole together, where Beast Boy spends the majority of the time singing "Fade Away" to her which later it deeply annoys her.
The trash hole appears again at the end of the episode, when Terra and Aqualad attack Beast Boy and Raven. When both Terra and Aqualad were in mid-attack, Beast Boy and Raven send Terra back into the trash hole for the third time, but this time with Aqualad.