Homo thread is a meme which gives Anonymous a chance to post his favourite /a/-safe homo images. Always predominantly male, despite the fact that homo could clearly apply to female pairings. Then again, yuri fandom is very strong on /a/ and doesn't really need an excuse to post their stuff.
The OP image is always one of Mugen from Samurai Champloo, entitled _homo.gif (though HOMO.gif seems to be an acceptable variation). Any straying from the norm will inevitably cause the Homo Thread to end in failure. Another thing worthy of mention is that these threads were generally regarded as pure mindless spam, and thread starters have been banned for them in the past. These feelings have been subsided somewhat recently - this may be linked to the fact that the Kyon x Itsuki hjiacking of Haruhi threads has been largely supplanted by Touhou hijacks and "viral marketing", which made male homosexual content on /a/ radically less common.
Variants on the Homo Thread have appeared dedicated to other topics, such as the "Manly Thread" (which often gets hijacked or derailed) and the "Hobo Thread" (which is usually ignored, since hobo threads are almost entirely made of reposts). A smirking Yabuki Joe from Ashita no Joe dressed in a long coat and wearing an old-style hat is always the OP picture for Hobo Threads.