the slightest bit of room; room to stand a gimlet on its end
Almost always used in negative constructions such as 立錐の余地もない or 立錐の余地がない, meaning there is absolutely no room. The literal image is of a space so small that even a gimlet cannot stand upright.
See also: 立錐の余地もない
The venue was so crowded that there wasn't even the slightest bit of room.
彼の机の上は書類で立錐の余地もない。
His desk is so covered with papers that there isn't room to stand a gimlet on its end.
余地 means 'room' or 'margin' in a general sense, while 立錐の余地 is a fixed literary phrase emphasizing an extreme lack of space.
From the image of a gimlet (錐) standing upright (立つ); the phrase literally means 'room for a gimlet to stand,' used to describe an extremely cramped space.