fraction of dissociation
Picture a bag of a hundred snap-together beads dropped into water; some pairs come apart, most stay joined. The fraction of dissociation simply answers: of all the units you put in, what share have actually broken into pieces? It is the percentage (written as a fraction between 0 and 1) of a dissolved substance that has split into its ions.
Formally, it is the amount of a compound that has dissociated divided by the total amount originally dissolved. A strong acid in water has a fraction of dissociation essentially equal to 1 — it comes apart completely. A weak acid has a fraction far below 1, meaning most of its molecules stay whole at any moment, with only a small slice ionised.
This single number ties together a lot of analytical reasoning: it sets how acidic a weak acid solution really is, and it explains why weak electrolytes behave so differently from strong ones. The honest and slightly surprising caveat is dilution: the fraction of dissociation of a weak acid rises as you dilute the solution. Spread the molecules further apart and a larger share of them break up — even though the total number of ions in the beaker goes down.
In 0.1 M acetic acid only about 1.3% of the molecules are dissociated at any moment (a fraction of about 0.013); dilute it tenfold and that fraction climbs to roughly 4%.
Diluting a weak acid raises its fraction of dissociation.
Do not confuse a high fraction of dissociation with a strong acid in the everyday sense. A very dilute weak acid can be largely dissociated yet still produce few hydrogen ions overall, because there is so little of it dissolved to begin with.