Why do I get angular cheilitis? Is it an infection?

Yeast. In addition to dr raff's answer, occasionally this is the result of a yeast infection which disappears with antifungal therapy.
Chelitis. Many conditions and factors can precipitate transient or chronic cheilitis, including overexposure to the sun, nutritional deficiencies, allergies, medications, dehydration, diet and certain systemic diseases. Transient cheilitis typically requires no medical intervention. Treatment for chronic cheilitis depends on the underlying cause.
Not usually. May be vitamin deficiency, may be overdryness of the edge of the mouth. Sometimes infection will occur secondarily.