There is probably a LARGE capacitor at the power input end of the ESC, which sits there uncharged until you apply power by connecting the battery. It then charges as fast as possible, giving the spark. for a few brief milliseconds, it is effectively a short circuit until it charges. An anti-spark connector does the connecting in two stages, the first through a resistor that limits the initial current below the spark forming level, the second is the real power connection but this happens to a fairly fully charged capacitor, so no huge current.
The sparks happen because as the connector points connect, they start with a very small surface area which is nothing like big enough to carry the inrush current and the contact points get very hot very suddenly. They are bits of the metal burning away. When the contacts are fully made, no problem until the day comes when the burnt bits get too big.