Secondary Relatives ?

Well, the general rule of thumb is that two chords can substitute for each other if they share 2 or more notes.

Looking at the normal major scale chords:

The vi, Am (a-c-e) can substitute for the I, C (c-e-g). Thus you change the progression I-I-IV-V to I-vi-IV-V, for example.

The ii, Dm (d-f-a) can substitute for the IV, F (f-a-c). So I-vi-IV-V could become I-vi-ii-V. Note that even though the melody contained a c, that note would just make the full chord Dm7 (d-f-a-c). The same applies to the Am/C substitution above.

Now, the iii (Em, e-g-b) is something of a special case and occupies a kind of middle ground in music. It shares 2 notes both with the I (C, c-e-g) which is supposed to sound like "home", restful, stable and the V (G, g-b-d) which is supposed to be "dominant", tense and harsh. So what to do with the iii? Well, people have used it in all kinds of ways, but mostly as a kind of halfway-I, a little movement, but not a lot. It lacks the necessary harshness to be a fully functional replacement for the V, but has been used as such anyway (Eleanor Rigby?) Used as a kind of I our progression above, I-vi-ii-V could become say, I-vi-iii-ii-V (vi and iii half measure each?).

The vii (Bdim, b-d-f) is simply a partial V7 (G7, g-b-d-f) and substitutes for it.

Chord substitution is mainly used to achieve variety in the harmonic background.

You may be referring to secondary dominants. The most basic way to approach this is to look at the chords in the harmonized scale. I will use C for example.

Chords within the key of C Major are based of the notes of the C scale.

C D E F G A B C

I C Major 7
II D minor 7
III E minor 7
IV F Major 7
V Dominant 7
VI A minor 7
VII G minor 7b5

Notice that the 2 (II) and 6 (VI) chords are minor 7th. The neat part is this can be figured out without knowing anything else other than you simply take the II chord and the VI chord and change them from minor 7 to Dominant 7.

Yes, I realize you are technically borrowing chords from other scales but it comes down to simply changing the 2 and 6 chords from minor7 to dominant 7.

No, secondary dominants is another thing...

You harmonized that scale wrong o.o

its B minor 7 b5

And secondary dominants are just using the dominant of X chord to resolve to it even if it is from another key
I V of I
C major 7 - G 7
V of ii
D minor 7 - A 7
V of iii ( and so on )
E minor 7 - B 7

F major 7 - C 7

G7- D7

A minor 7 - E 7

Bmin7b5 - F# 7

Here's an older thread on it: Secondary relative minors