The President can appoint someone as ambassador to another county; that means to give them the job or recommend them for it.
It must be nice to be appointed. Usually, people who want a job have to send in applications, do interviews, and jump through lots of hoops. Appointing is different: someone with the power to appoint can usually just give you the job. In some cases, appointing isn't a sure thing and means something closer to "recommending" — but it still beats filling out all those applications. It takes power to appoint people, which is why world leaders are often the ones appointing.