In best subsets regression, Minitab uses a procedure called the Hamiltonian Walk, which is a method for calculating all possible subsets of predictors, one subset per step. That is, Minitab calculates all 2**m - 1 subsets in 2**m - 1 steps, where m is the number of predictors in the model. Minitab evaluates a different subset regression at each step.
Each subset in the Hamiltonian Walk differs from the preceding subset by the addition or deletion of only one variable. The sweep operator "sweeps" a variable in or out of the regression on each step of the Hamiltonian Walk, and calculates the R2 for each subset.