When Catherine was born, her father Henry Beddoes (Denholm Elliott) signed a pact to put her in Father Raynor's care until she is 18 when her soul will be given to the devil. The snake scene happens after Beddoes asks Verney to hide Catherine from Father Raynor. Raynor suspects that Beddoes is trying to back out of his promise by hiding Catherine so he calls him on the telephone. When Beddoes won't talk, Raynor wraps a rope around the phone. This magically conjures a snake wrapped around Beddoes' hand, which terrifies him. Raynor threatens to let him die unless Beddoes tells him where Catherine is hiding. Beddoes gives in and as soon as he tells Raynor the snake disappears.

The snake is a harmless gophersnake, but we are probably supposed to think it's a venomous snake.

You can watch the whole movie and read more about it at TheSilverScream.com. The snake scene starts at roughly 41 minutes.