The primary similarities between a novel and a drama are that they both have plots, complete with rising action, climax, falling action, and resolution; they both have conflicts, characters, and themes. They both tell stories, essentially—they simply differ in the manner in which they tell it.
A drama is meant to be performed, to be seen and heard. It does not typically have a narrator, someone who can interpret characters' actions or thoughts, as some novels do. A novel will always have a narrator, even if that narrator can only report what is visible to the protagonist. A drama is going to rely on dialogue as its main mode of conveying information. Everything the audience needs to know must be spoken aloud, and so characters sometimes deliver soliloquies or asides in order to share their internal thoughts and feelings with us. A soliloquy is when a character is alone on stage, speaking his or her thoughts aloud. An aside refers to moments when a character speaks to him or herself, to another character, or to the audience, and, by convention, those characters who are not supposed to hear do not hear (even if the actor is standing close enough to hear what the other says).