Urination was the process by which urine was disposed from the body through the urethra, in humanoids as well as certain other creatures. To pee or to "take a leak" were slang terminologies originating from Earth that referred to the act of urination.
In 2063, Zefram Cochrane conspired to escape the uncomfortable circumstances by stating that he had to take a leak as a ruse. Confused, Geordi La Forge stated that he couldn't detect a leak with his ocular implants. Cochrane explained that to "take a leak" meant to eliminate or pee. (Star Trek: First Contact)
In 2152, a minor diplomatic incident was caused when Porthos, the pet dog of Captain Jonathan Archer, urinated on the sacred trees of the Kreetassan people. While Archer had, in annoyance, mentioned the idea of urinating on these trees himself, due to the negligence of the Kreetassans to ensure Porthos's safety to pathogens in their atmosphere, the issue was resolved after Archer performed a Kreetassan apology ritual (ENT: "A Night in Sickbay").