Secondary Dominants
Secondary dominants are major 2, major 3, or major 6 chords that often act as a temporary dominant (5 chord) to another chord besides 1. The most popular secondary dominant is a major 2 chord.
Jingle Bells Chorus (in C): 1 1 1 1 / 4 1 2 5
The D major here acts as a temporary '5' chord to the following G (as if G were temporarily 1).
Another common example is a major 3 going to a 6m, as in Leonard Cohen's Hallelujah. In C, this would mean our 3 chord, E, acts as a temporary ‘5’ leading to the 6m (Am). A dominant (5) chord will always be major, even if it leads to minor chords.
V: 1 6m 1 6m / 4 5 1 1
1 (45) 6m 4 / 5 3 6m 6m
Secondary dominants often have a dominant 7 added to the chord (a note a minor 7th above the root). This strengthens the pull from it to the next chord by adding a bit more tension.
Here are some more examples of these chords in use:
Michael Kiwanuka's Home Again:
In G, the 3 is a B7, moving to Em.
James Taylor's Your Smiling Face:
There are two kinds of secondary dominants in this head (on the 3rd line): The 2 going to 5 and 3 going to the 6m. Dominant chords (5 chords) are always major, even if going to a minor chord (more on this in this explanation on minor keys).
Besides giving us some harmonic diversity, secondary dominants also provide us with smooth, connected walking bass lines (when inverted), like in the above example.
Sometimes major 2, major 3, and major 6 chords don't act like temporary 5 chords and can be followed by really any chord just because it sounds good, as in Tom Petty's American Girl:
V: 1 2 4 5 / 1 2 4 5