This word comes from Oogling, which is staring at someone for a period of time because you have a crush on them, or they are attractive.
It's a game of endurance, where both person creates a sweeping motion on the other persons hand, while calling out oooooooooooogly, after of which the game changes, with both players flailing their fingers into each others.
There is a variation of the game, where finger nails, or "claws" (where the name comes from) are used to dig into each others fingers. This is called Clawgly, and is frowned apon in the Oogly community.
"HEY!, No clawgly!"