Originally, you got "on board" a ship. Now, we also speaking of getting "on board" a bus, train, or plane. To get "on board" means to join a group of people who are all going together in the same direction. Thus, it can be used as a metaphor for "agreeing with a group." A manager who is trying to get enthusiastic agreement from a group of workers might say "I want to have a discussion and make sure that everybody is on board with this." It means "I want to be sure I've convinced you all. I want to be sure I have your cooperation, not just because I am ordering you to do this, but because I've convinced you that it is the right thing to do." It means "join the group of people who are all going in the same direction on this." "I'm not fully on board" means "I don't completely support this idea." A related idiom, used in business circles, is "buy-in." To "get somebody's buy-in" or "to get them to buy into the idea" means the same thing as "getting them on board." It means to win their full and enthusiastic agreement.

It essentially means "to agree with," usually with regard to some action. Not being on board with the new high five thing means that the person does not agree with the new high five activity going on between people, or does not want to do it themselves.