The begin dialog can appear at the start of games that are set to use the no-luck cyclic move order. In no-luck cyclic move order, the speed at which each player plays the first turn determines the game's move order. This speed is measured from the time each player clicks "Begin" on the begin dialog to when they commit orders on their first turn (or commit territory selections during a manual distribution game.)
The begin dialog can be skipped by checking the "don't show this again" box, or on the Settings tab. When it's skipped, your speed will be measured from when you first open the game.