A non-inertial reference frame is like being in a car that is going really fast and you're trying to play catch with a ball. When you throw the ball, it doesn't go straight to the person you're throwing it to because the car is moving and affecting how the ball moves.
In the same way, a non-inertial reference frame is a way of looking at motion when there is some kind of acceleration or rotation involved. This could be like being on a merry-go-round or a Ferris wheel, where you can feel yourself moving in a circle.
When we talk about motion in a non-inertial reference frame, we have to take into account the forces that are acting on the object we're interested in. This is because these forces can cause the object to move in a different way than it would in a non-accelerating or non-rotating frame.
So, to summarize, a non-inertial reference frame is a way of looking at motion when there is some kind of acceleration or rotation involved, and we have to take into account the forces that are acting on the object we're interested in.