The default octave position that FastChords places a chord favors the left hand. FastChords is often used to play from lead sheet music, where songs are written with just chord symbols and melody lines. The chords are played with the left hand and the melody with the right hand.

Optimizing a chord means finding a chord inversion and octave position that minimizes left hand changes from the previous chord. 

This is something you could do manually by inverting the chord and changing its octave position, but the program can do it a lot faster.  Not just for a single chord, but also for the entire song.

Optimizing a chord does not mean it will sound nicer, that is a subjective judgment.  It simply means that it will be easier to play the chord given the chord that precedes it. 

When a chord is optimized it gets an optimization score: 

The score reflects the cumulative number of keys the fingers of the left hand will have to travel to change from the previous chord.
 

The smaller the optimization score, the easier it is to play the chord.  An optimization score of zero (0) -- which is possible -- means that no finger changes position from the previous chord.

Before optimization

The Am7 chord has an optimization score of 13 (the chord is not optimized).

After optimization

the Am7 chord is optimized to

Am7/C and the score falls down to 1.
 

Notice only one finger needs to change position to go from the C7 chord to the Am7/C chord.