A crack spread is the value of refined products minus the crude used to make them. It is the market's standard shorthand for refining profitability and the instrument a refiner actually hedges with.
The best-known version is the 3-2-1: three barrels of crude producing two barrels of gasoline and one of distillate. Those proportions are a rough stand-in for a typical US refinery's light product yield, chosen because they are simple and because the underlying contracts are liquid.
Now the caveats, because a crack spread is a proxy and the gaps matter.
The regional variants exist because the assumptions differ by region. A European refinery skews toward distillate and prices off Brent, so a 3-2-1 built on WTI and US products describes it poorly. Singapore cracks are struck against Dubai. Using the wrong regional crack to reason about a refiner is a category error that produces confident, wrong conclusions.
Cracks also carry the seasonal signature of the products underneath them. Gasoline cracks typically strengthen into the northern summer driving season and weaken after it; distillate cracks strengthen into winter heating demand. Those patterns are strong enough to be worth knowing and weak enough that trading them naively is a good way to lose money in the year the pattern does not hold. See demand seasonality.