A thinko is a silly error or a blunder. The most usual usage is for moves that were decided upon in a rush or without much thought (whether or not the alternatives were given much thought). A thinko usually causes the player to exclaim to themselves, soon after, "What was I thinking!", perhaps even before the other player has moved.
In online games, many players will not grant an undo for a thinko, while most players (though not all) will readily grant an undo for a clicko if it is requested immediately. A prompt request distinguishes the clicko from a thinko whose faults may more slowly impinge on the player's consciousness.
This is a modern back-formation in English. The phrase typographical error (inadvertent insertion or deletion or change of a character in text) is often abbreviated as typo. The analogous word was then derived from think.
Velobici: Thinkos that I have inflicted upon myself, result in a nearly involuntary exclamation or expletive, as soon as it hits the board. This is a problem, for me at least, because there isn't a noticable time difference between playing a clicko or thinko and hitting myself in the head! Clickos sometimes are played on obviously useless points. These clickos are easy to recognize. Others appear to be no different than Thinkos. (A famous example is Isumi's play against Hikaru in the professional qualifying tournament in Hikaru no Go.)
Hikaru79: Ah, but that WAS a thinko. He was so wrapped up in thinking about Touya Akira seeing Shindou as a rival, that he was playing absently. As soon as he laid the stone, he went "Oh! Of course, I should atari from the other side" and undoes his mistake illegaly. Although he realized his thinko immediatly, it wasn't like he accidently dropped the stone in there or something.