'Onboarding' is a 'neologism', or newly invented word, meaning the process of getting passengers onto a plane or other mode of transport. I've never heard it before, but it's clear what it means. English is a very flexible language, and new words are created the whole time by changing one part of speech into another. In this case, the adverb 'on board' has been turned into a verb ( to 'onboard') and then it's been turned into a gerund and used as a noun. If the 'customer onboarding process' is fully digitised, it means that there are no paper tickets involved and nobody to check your tickets - it's all computerised. Basically, it sounds like some kind of online flight check-in, as Dan suggests.

To me it's sounds like processing / getting passengers on the plane or bus etc. Some kind of online check-in maybe?