Role conflict looks different in various contexts. At the center of the issue is that a person feels "pulled in two directions," so to speak, based on two different senses of obligation.
Consider this scenario. You have a supervisory position at work, and your incredible friend Noelle works there as well. Your boss thinks you do outstanding work and depends on you to lead people well. Unfortunately, Noelle is struggling with her personal life, and she's often late and usually unfocused, making lots of mistakes. People begin complaining to you about Noelle since you are her supervisor. Noelle's personal life gets worse, and she becomes depressed, telling you that work is the only thing saving her at this point. Your boss tells you that you're going to have to remediate the situation with Noelle. You now have two competing roles: good employee and good friend. It's tough (or impossible) to be both in this scenario.
Sometimes we experience role conflict because the expectations of the role are ambiguous or poorly defined. Consider the mom who works full-time and also wants to be a "good mom." Because stereotypical expectations abound in our society, she may attribute the role of "good mom" to things that conflict with being an employed mom. Perhaps she misses a soccer game. Maybe she feeds her kids takeout four nights per week. Maybe she has to reschedule her daughter's optometrist appointment because she herself has a presentation at work that same day. At this point, she may feel that her role of employee and her role of mom create conflict with each other.
The more roles and responsibilities one has, the more likely one is to feel conflict between those roles.