A mutual connection is someone who knows both you (or your team) and the buyer you want to reach. Because they sit between both sides, they can make an introduction, which makes them the starting point for most warm paths into an account.
Not every shared contact is useful. A mutual connection built on a shared employer and overlapping tenure can carry an introduction; an old social-network accept neither party remembers cannot. Telling the two apart is the job of relationship intelligence.
Once you have found a real mutual connection, they become the connector on your warm path. The skill is making a lightweight ask. See how to leverage mutual connections and how to ask for a warm introduction.
Via finds the mutual connections you did not know you had. It looks across your whole team's relationships, distinguishes the real ones, and shows who can introduce you to a given buyer and why that path is strong.