Yes, lying on your sides facing in the same direction together and touching closely, like 2 spoons nested in a drawer, most commonly in bed. Best done naked. That's the contemporary definition, and how most gays use it.
There is an older definition, used mostly before WWII in the US, that means to kiss and cuddle in a more general sense, applied almost exclusively to an unmarried couple who were dating. A pair sitting together on a park bench or on a sofa could be spooning, as a kind of preliminary lovemaking or even foreplay.Gay spooning in bed:
(Not sure how long Photobucket will let that stay online)