The term coattail effect refers to trickledown support that the other candidates on a ticket receive due to the support that a more popular candidate on that same ticket receives. It is typically a candidate running for a higher office increasing the support for a candidate running for a lower office.
The term coattail effect is also used, although less frequently, in reference to someone in politics who benefits from having worked for or with another more powerful and influential political figure.
Governor Bob McDonnell was so popular in Virginia that any Republican running for lower office that year could easily ride his coattails.
The back of a suit jacket (today a morning suit or a formal cutaway tuxedo) a split in the back forming two "tails." The mental image of the coattail effect would be that of the less powerful politicians clinging to the coattails of the more powerful politician hoping to benefit from his/her popularity.