Intervals are often judged according to their strength or stability. In reality, these are synonyms for what your mind perceives as CONSONANCE. The more consonant an interval sounds, the more stable or strong it seems to be.
The reason for this phenomenon is actually pretty easy to grasp.
In equal temperament tuning (most common), each INTERVAL step is considered to be 100 cents from the previous/next INTERVAL step. That means that between each half-tone INTERVAL there are 100 smaller, individual steps. Each of these 100 steps actually represents a small change in the frequency of the sound.
Looking at the CHROMATIC scale, you can see how this works.
In the graphic above, the distance from C to F (P4) is 500 cents. The distance from C to G (P5) is 700 cents. The distance from C to C (OCTAVE) is 1200 cents. These variations represent the differences between the notes in the form of a ratio.
It’s really not as important to remember all the numbers as it is to realize that each 2-note combination (INTERVAL) has a specific sound and that each of these sounds is unique and distinguishable by the human ear.
If you’d like to see the math, the following link makes it semi-understandable (http://legacy.earlham.edu/~tobeyfo/musictheory/Book1/FFH1_CH1/1M_RatiosCommas1.html)
As you move from one note to the next on the CHROMATIC scale, the sound will become increasingly sharp until it reaches the next note. If descending, the sound will become increasingly flat.
The following graphic shows a cutaway view of the cents going from C# to D.
A perfect example of changes in cents in action is when you bend a string on a guitar. If you have a tuner (clip-on or otherwise that has a cents display), turn it on, fret a string and then bend it slowly in either direction. What you should see on the turner is the change in the cent values as the string changes shape.