Being "on the ticket"

I'm currently watching House of Cards and I keep hearing the expression "being on the ticket". It's always in relation to a presidential candidate, but I'm not quite sure what it means, particularly because of this bit of dialogue:

— Did he offer you a cabinet position?

— ...

— More than that?

— ...

— He offerred to put you on the ticket, didn't he?

You may be interested in this Wikipedia article: Ticket (election). The second sentence here is particularly relevant to your query:

A ticket refers to a single election choice which fills more than one political office or seat. For example, in the U.S., the candidates for President and Vice President run on the same "ticket", because they are elected together on a single ballot question rather than separately.