The easiest way to picture it is the correlation between meter and centimeter.

1 meter is 100 centimeters, but 2 meters are not 101 centimeters but 200. The relationship is linear because you use a linear function to convert from one unit to the other. In this case it's meter = 100 cm.

In case fahrenheit it's more complex to calculate in your head, but simple if written down: Celsius = (Fahrenheit - 32) x 5/9.

To imagine a non-linear correlation you can think of something like how the amount of chocolate you eat relates to your enjoyment.

You eat a bar of chocolate, that's cool. You eat two, it's better. But as you keep eating more and more you start to get full and by the time you eat your 25th bar of chocolate you'll want to puke. So if you'd want to illustrate it on a chart, the line would start to rise and quickly drop at a point the more chocolate you eat.

The relationship would be linear if your enjoyment would increase by the same logic regardless of how many chocolate you ate (or more precisely, if there was a linear function that you could use to calculate it).

Edit: clarification