In political terminology, a "Vanity Candidate" is someone who runs for a prominent political office from a desire for attention or fame, without having a serious chance of winning the office.
Vanity candidates can run for a variety of reasons: sometimes they want to bring attention to their positions, and if they are strongly in favor of only one position, they are a single issue candidate. Sometimes they have a financial motive: even a spurious candidacy can lead to renewed stature that can increase book sales or lead to a job as a news analyst. And sometimes vanity candidates seem to be interested in the sheer fun of running for office.
There is a sliding scale of vanity in a candidacy: almost all politicians have attention as a motive, but it is usually tempered by realistic expectations of electoral success. There are some candidates who are long shot or dark horse candidates, but who are not "Vanity Candidates". But there are many candidates (although I will refrain from naming specific names), who are obviously not interested in holding office as much as they are in running for office.