The large teardrop-looking thing that appears on, or next to, an anime or manga character's forehead. Primarily used with the super deformed or "SD" style of animation, a sweat-drop denotes that a character is embarrassed, incredulous, or possibly relieved, depending on the character's facial expression -- good analogies might be someone rolling one's eyes, or exhaling a held breath. As with most translation, the sweat-drop doesn't really have a one-to-one correspondence with anything in American animation. Other stylized expressions of emotion in anime include the vein-throb, the facefault, and the nosebleed.
"Sweat-drop" may also be used as a verb; in this case, it merely indicates the action of a sweat-drop appearing.