Tonality is the relationship of chords and notes based on a "key" or "tonic" (first note of a scale). When you are using the "C" scale, or in the key of "C", the tonal center or tonic would be "C". If in the key of "F", then the tonal center or tonic would be "F" and so on.
The tonal center can be either Major or Minor depending on whether you are in a Major or Minor key. Example: When in the key of "A minor", the tonal center or tonic would be "A".
In tonal music, which is centered on tonality, the use of "temporary keys" may also occur during a song or score. Simplistic music such as country, rock and modern dance music, very seldom make use of any temporary keys. These types of music tend to stay seated in one key throughout the entire song. Jazz music, including what are known as "standards", and more sophisticated types of music, such as orchestral or classical music, make regular use of temporary keys during the song or composition. Temporary keys meaning, for a moment in the composition, the center of the key shifts temporarily to another key, but still the overall composition will ultimately center on the tonic or key signature in use for the song.
One of the ingredients the ear uses to determine a key center is chord progressions. The chord progression of "I, IV, V" is at the center of determining the tonality of the music. For example, country and rock music use this "I, IV, V" progression throughout the entire song (modern dance music may use even less). Jazz music tends to use a "IImin7, V, I" progression to establish it's tonal center which is basically an extension of the "I, IV, V" progression by extending the "IV" chord to become the "IImin7". If you add the "third" below the "IV" chord, it produces the "IImin7", so the ear reacts to this sound similarly to the "IV" chord to establish the tonal center.
In Jazz music, the "IImin7, V7, I" progressions will frequently make use of "temporary keys". Meaning for short segments of the song, this chord progression will be "borrowed" from another key. For example: In the key of "C", you will have "Dmin7 (IImin7), G7 (V), C(I)", followed by something like "Gmin7, C7, F". This second progression makes use of the temporary key of "F" while the key signature of the song remains in "C". Take a look at chord progression in some Jazz music or "standards" and you can clearly see this use of temporary keys throughout the entire piece.
Lastly for this brief overview of tonality, we need to take a look at the use of chords in Minor Keys, or Minor Tonality. It is standard practice to alter the "V" chord to major while in the minor key. If we look at the scale in minor, we quickly see that the chord tones used to make up the "V" chord would create a minor chord naturally, Our ear is used to the major "V" chord because it provides the leading tones of the "tri-tone", which are "FA" and "TI" in solfege. These two tones want to resolve which lead you to the tonic. Examples: In the key of "A Minor", we typically see and hear "Amin (Imin), Dmin (IVmin), E7 (V7 - altered to major)", or in jazz keeping with the "II, V, I" concept, we have "Bmin7(b5), E7(b9), Amin". With the "V" chord, in this case E7(b9), altered to use a major third (the b9 and other alterations on the V chord appear in the scale in use at the time).
The topic of tonality is really quite simple, so simple it is difficult to explain. The best approach to use in understanding this concept of tonality, tonics, key centers and temporary keys is to take the information provided here and do some detective work on your own by examining chord progressions in what are known as "standards". Have a look at some songs such as "How High the Moon", "All of Me", or other similar such standards and detect the use of all the temporary keys used throughout these pieces.