Onboard is one word (sometimes hyphenated—on-board) when it comes before the noun it modifies (e.g., onboard radio, onboard computer). Elsewhere, writers usually make on board two words. For instance, one might write, “We brought a radio on board so we could have an onboard radio.”
If it helps, think of it this way: the two-word on board usually means the same as aboard, and aboard would usually work in its place. Aboard would not make sense as a replacement for onboard. Try it with the examples below.
Examples
Onboard
Justin boasts an onboard 3-D camera system for analyzing points in space. [Wired News]
Although the airline grabs headlines for threatening to charge people to use onboard toilets or save money by dumping co-pilots, it normally turns to conventional ruses. [Guardian]
At one highway fill-up, the onboard computer showed I had a range of 880 km. [National Post]
On board
President John F. Kennedy called Shepard after he was taken on board the aircraft carrier that retrieved him from the ocean. [USA Today]
San Pietro was being sailed by the remaining crew on board. [Stuff.co.nz]