Authority in Christ's church is so key because it allows saving ordinances, such as baptism, to be performed and be valid in the sight of God. There was a reason for Christ going to John the Baptist to be baptized, because John held the priesthood authority, or in other words he was authorized to do so. Not just anyone can perform baptisms, it is like an ice cream man turning on his music and flagging you down to give you a ticket for speeding, he does not have the authority to do so. But when a police officer turns on his lights and sirens and pulls you over to give you a speeding ticket, he has been authorized to do so. Now, priesthood authority is not gained by any amount of school or receiving a certificate of certain achievement.(Hebrews 5:4) Priesthood authority is given from one who currently holds that priesthood and when authorized he can then give it to another. For example, an unlit candle cannot simply catch flame, instead you must take another candle that is already burning and use it to light the wick of the other. Similarly, that is how it works with priesthood power: there must be a source.
The time after the death of Christ and His Apostles when the priesthood authority was taken from the earth is called the Great Apostasy. It wasn't until John the Baptist appeared to Joseph Smith on May 15, 1829 and restored the priesthood authority to Joseph Smith that he could then perform valid baptisms. I know that this priesthood authority is found in the Church of Jesus Christ of Latter-Day Saints. Baptism is necessary to return into the presence of God and must be performed by proper authority. Christ lives and is our Savior, this is His authority and His church.