What is an arms race?
Anytime two or more countries try to out produce each other in a given type of weapon or in overall military capability (e.g. one country may concentrate mostly on building tanks while another may concentrate mostly on building aircraft, while yet another concentrates mostly on building their infantry capabilities - this would be an asymmetric arms race).
In today's world, an arms race, means an escalation in the production of weapons and or weapon systems. This is a costly "race", without a doubt. It also implies more research on better (deadlier ) weapons. It gives rise to more profits to defense industry profits.