What effect would an "electrical failure" have on an aircraft?

On the news they said that the Airbus that has tragically disappeared reported an electrical failure before they lost contact. What effect would this have had on the plane? What would this have done to the safety of the pengers? Is that a major fault or would it not have had much of an effect? Also, what is a "Mayday" call? They said it was never received. What is this?