A good analogy for the effect of concentration on reaction rate is a walk through the hallway at school.
You are more likely to "bump into" someone to speak with at recess time when there are lots of people in the corridor than you are when you are on your way to the washroom when classes are in session.
The analogy can be extended by imagining a situation where 100 people who are milling about in the gymnasium are asked to move into a classroom. There ought to be a lot more collisions due to milling about in the classroom than in the gym.