To dream of things being off in the distance represents long term goals or your perception of things to come in the future. Alternatively, a long distance could reflect a large amount of work you feel you have in front of you.
To dream of someone being far away from you may represent emotional distancing you feel in a relationship. You may feel alone. Alternatively, it represents something that is unattainable or something that is difficult to achieve. Not feeling popular.
To dream of intentionally keeping your distance from someone may reflect feelings about issues you want to avoid. Avoiding a fight. If people in your dream intentionally keep their distance from you it may reflect feelings about other people not liking you.
Example: A man dreamed of keeping his distance from someone. In waking life he wished to avoid having a meeting or confrontation with the person.
Example 2: A woman dreamed of studying a volcano from a distance. In waking life she was in a fight with her husband and choose to watch hi sbehavior closely without talking to him to decide the best time to defuse the fight as she felt that he was too close to erupting with anger.
Example 3: A young woman dreamed of being at a party and seeing people keeping their distance from her. In waking life she felt like a geek at school and people didn't think she was cool enough to know.