Let's take this chord progression in the C major key and embellish it using secondary dominants:
First, let's prepare the IV degree chord by preceding it by it's dominant. The IV degree chord is F major and C7 is the dominant chord of F:
We write V / IV to indicate a secondary dominant of the IV degree. We refer to these chords as V of IV or V of V, etc.
Now, let's do the same with the V degree chord. The dominant chord of G is D7:
By using these secondary dominant chords, we have added some harmonic interest to the original chord progression.
The first measures of Beethoven's first symphony are an excellent example of secondary dominants use. Note the use of secondary dominants of the IV and V degrees:
Here we show all the secondary dominant chords of all the degrees in the C major key:
Diminished seventh chords have a similar harmonic function. They too can be used as secondary diminished seventh chords. Here we show all the diminished seventh chords in C major: