Why are there seven games in the Stanley cup?

Seven games is the maximum number of games that can be played before at least one team must have won four games in total (where all games must end in a winner and loser).

The schedule begins as four games, as this is the minimum number required for a team to win the series outright. After these four are played, extra games are added until it is possible for one team to win the series by winning all remaining games, with seven being the maximum number required to ensure a team has won the series.

As to why the limit is four wins, and thus seven games required, instead of say 3 and 5 or 11 and 21: because that is the amount the original organisers chose.