As you're speeding down the freeway, all of the sudden you see an ice cream truck pull up next to you with his music BLASTING like crazy!!! He's signaling for you to stop and pull over, so you do, thinking he might be giving you some free ice cream! Instead...
By revelation and by the laying on of hands (see Exodus 28:1 and Articles of Faith 1:5).
Aaron didn't receive his authority by paying to go to school to receive a degree (like Simon the magician attempted to do [see Acts 8:18-20]) . The twelve disciples whom Christ gave the priesthood to did not receive their authority by simply feeling inspired to go and do something (Christ taught them "Ye have not chosen me, but I have chosen you, and ordained you..." John 15:16). They received the priesthood through Jesus Christ, who held the authority, by the laying on of hands.
Why is authority important? Even though the ice cream driver was trying to do what was right and keep the road safe, and though his intentions were perfectly good, he did not do it under the direction of the state. When Jesus Christ was baptized, he went "from Galilee to Jordan unto John, to be baptized of him (Matthew 3:13)." Christ came from Galilee to "Bethabara beyond Jordan (John 1:28)", which is about 50 miles, to be baptized by John the Baptist because he held the authority to baptize.