A dramatic monologue is text meant to be spoken by a character in a play, but sometimes this device is used as the "speaking voice" of dramatic poem or verse. The monologue reveals a character's point of view or his/her feelings and should reveal something new to the audience or reader about that character. A monologue is different than dialogue in that it is not a back and forth conversation between two or more characters. It also differs from a soliloquy which is spoken by a single character who is alone onstage. A monologue is spoken by a character when other characters are present onstage.
Here's a monologue spoken by Olga from Anton Chekhov's The Three Sisters, the first speech at the very beginning of Act One.
It's just a year since father died last May the fifth, on your name-day, Irina. It was very cold then, and snowing. I thought I would never survive it, and you were in a dead faint. And now a year has gone by and we are already thinking about it without pain, and you are wearing a white dress and your face is happy. [Clock strikes twelve] And the clock struck just the same way then. [Pause] I remember that there was music at the funeral, and they fired a volley in the cemetery. He was a general in command of a brigade but there were few people present. Of course, it was raining then, raining hard, and snowing.
Hope this helps!