An inertial frame of reference is one that is travelling at a constant velocity or is at rest.
A non-inertial from of reference is accelerating and the traveller is experiencing some sort of force.
Now, get in your car (preferably with someone else driving). Take off your shoe (hold your nose) and dangle the shoe by its lace and off you go.
When the car is accelerating, you will find that the shoe does not hang straight. So, when you are speeding up, slowing down, or changing direction, the shoe will act like an accelerometer and not hang straight up and down. The greater the acceleration the more the shoe will move from the vertical.
Now, stop the car. The shoe hangs vertical. Speed up and travel with a constant velocity, the shoe hangs vertical. These are both inertial frames of reference.
With the use of a simple accelerometer (such as a shoe on the end of a shoelace) you can distinguish between inertial and non-inertial frames of reference.
Hope this helps.