A wedge is the small, specific opening through which a startup enters a market it eventually intends to expand across. Toast started as a restaurant POS before becoming a full restaurant operating system. Square started with magstripe card readers for tiny merchants before becoming financial infrastructure. The wedge is small enough to win, but adjacent to enough territory to grow.
The wedge is both a positioning and a sequencing question: what's the smallest beachhead the company can dominate, and what's the natural expansion path from there?