“My contact at Microcorp says that they're on board.”
You're helping to plan a conference. Your job is to find sponsors. You've heard that another company has agreed to sponsor the conference, so you say this to one of the other conference planners.
My contact at Microcorp says that they're on board.
A "contact" is someone in an organization whom you are able to speak with. Your contact can answer questions about the organization, or pass information on to other people in that organization.
For example, if your company uses software that's made by another company, you might have a "contact" at the company that made the software. The contact might be one of their salespeople, or one of the engineers who built the software.
We talk about "having" a contact:
Do you have any contacts at any local newspapers or blogs that you can ask about publicizing the event?
Contacts "belong" to someone:
I'll ask my contact in the sales department.
When someone joins a project or a team, you can say that they are "on board".
A: We'd really love for you to join us.
B: Who else is on board?
A: Well, Takahashi, for one.
You can also use the phrase "on board" to talk about whether someone agrees with an idea:
If you're considering borrowing money, I'm not on board with that.
The phrase "on board" originally mean that someone was on a sailing ship.