The quick change moves one bar of the twelve-bar. Bar two, which stays on the home chord in the standard form, goes to the subdominant instead, and bar three brings the form straight back. From bar three onwards the quick change and the twelve-bar are identical. The names it goes by, quick change, quick to four or quick four, all say the same thing: the subdominant arrives early.
What the one bar changes
Put this table beside the twelve-bar's and only one row differs, but that row changes more than a chord name. In bar two the flat third stops rubbing, because over the subdominant it is the chord's own flat seventh. The fourth of the key, which rubs against the home chord's third, becomes the new chord's root. The fifth turns into a ninth, a colour note. And the flat seventh, a chord tone over the home chord, now rubs a semitone above the subdominant's third. Two rubs leave the bar and one arrives, so the bar is calmer without being calm.
That is why the counts above differ from the twelve-bar's by exactly one bar's worth: one more colour reading, one fewer rub, and one more bar in which the flat third belongs to the chord. The chord tones stay level, three in the bar either way.
How it feels to play
Over a slow shuffle, four bars of the home chord can hang for a long time, and the early move gives the rhythm section somewhere to go before the first line is half over. It also hands whoever is playing the melody one bar where the blue third is suddenly a chord tone rather than a rub. Listen for the lift into bar two and the snap back in bar three; the table shows exactly which notes changed their job when it happened, in whichever key you choose.