A "thread" is a series of related email messages.
The Ignore Thread feature is especially useful for mailing lists. It lets you skip reading the rest of a conversation you're not really interested in following, while still being able to keep up with all the other conversations.
To ignore a thread you select Message > Ignore Thread, or simply use the K (for "kill") keyboard shortcut. That will mark all the messages in the selected conversation as ignored. The ignored messages aren't deleted, but once you come back to the folder they won't be shown in the thread pane (by default). If there are further replies to the same conversation, these replies won't trigger a new mail notification.
Ignore subthread works similarly to the Ignore Thread, but ignores only messages that are replies to the subthread starting from the selected message. This can be used to ignore otherwise interesting conversations that get off topic from a certain response.
If you decide you do want to see ignored threads, perhaps temporarily, you check View > Threads > Ignored Threads. To again stop seeing ignored threads simply uncheck View > Threads > Ignored Threads.
To un-ignore a single thread that has been marked ignored, select a message in the thread and uncheck Message > Ignore Thread.
See also: Blocking a sender