Consonance and Dissonance
One of the founding principles of tonality is the idea of consonance and dissonance. There is disagreement on the theoretical basis for this concept, but what is certain is that it has become so firmly ingrained in our culture that it is central to the way we understand tonal music.
The reasons why are less important than the fact that within the Western musical tradition dissonant intervals are felt to be somehow unstable, in need of resolution to a less unstable interval. A consonant interval could therefore be described as stable - it does not feel like it needs to resolve. Consonances are sometimes described as being inherently more pleasant to the ear and dissonances as less pleasant.
In general terms, major and minor seconds (and sevenths - their inversions) are understood as dissonant, as are augmented fourths. Major and minor thirds and sixths and perfect fourths and fifths are understood as consonant. However, as discussed in the main style section of this site, the extent to which any interval is considered dissonant changes in different styles.
An exception to this classification is when there is the interval of a fourth above a note in the bass. Suspensions are a good example of a fourth being treated as a dissonance.