What is the practice of forcing people into the navy called?

The practice used in the British Navy (among others) was called impressment and was used to fill ship's crews. It was also called "pressganging" for the "press gangs" (impressment teams) that performed the practice, often with violence or threats of violence. Impressment of nominally British-born American sailors was one cause of the War of 1812.

The practice is colloquially called "Shanghaiing" - in the days of sailing vessels, ship Boarding Masters (responsible for finding able bodies for their ships) would literally kidnap much needed manpower from the bars at various ports. Those engaged in the practice of shanghaiing sailors were known as "crimps". Though primarily associated with the US northwestern ports, the term applies to any similar practice of impressing sailors into service against their will. It's hard to fight when you're stuck on a ship at sea also; your choices are either work or hope you can swim to shore.

The term is believed to have originated from the port destination of Shanghai, China, a common destination for ships with abducted crews.

The practice survived into the 20th century, until laws were finally passed in the US that ended the practice. However, it was normal practice in Iceland up until the 1970's