Everything you see on stage is the work -- directly or indirectly -- of the Artistic Director. This is the person who chooses which ballets to perform; hires and casts the dancers; selects the designers for sets, costumes and lighting. S/he also hires outside choreographers to make new ballets, and the ballet masters and teachers. Sometimes the Artistic Director commissions a new ballet from him/herself, but it is not necessary to be a choreographer in order to be an Artistic Director.
In addition, the Artistic Director is generally the most visible single behind-the-scenes personality of the company and can be called on for fundraising and publicity.