An endorsement is a form of public support or approval. Endorsements are given to politicians and products.
If you give something an endorsement, you're basically saying "I approve of this person or product." Celebrities give politicians an endorsement if they think you should vote for them. When celebrities do commercials for products, those are also endorsements. If someone puts their fame or name behind something, they're endorsing it and giving their approval. That goes for checks, too: when you sign one you've just written, you've endorsed it.
n formal and explicit approval
O.K., OK, okay, okeh, okey
an endorsement made in a passport that allows the bearer to enter the country issuing it
the phrase used by the official censor of the Roman Catholic Church to say that a publication has been examined and contains nothing offensive to the church