“All the prophets testify about him, that everyone who believes in him receives forgiveness of sins through His name.” - Acts 10:43 NIV
Over and over, I have stared at these words, trying to pick them apart, in absolute awe at this simple statement: everyone who believes in Him receives forgiveness of sins through His name.
If you search for the definition of forgiveness, you'll find something along the lines of "the conscious, deliberate decision to release feelings of resentment, anger, and vengeance toward someone who has harmed you."
Can you think of someone who has personally harmed you? Did you offer them forgiveness, or did you hold a grudge? If you chose forgiveness, was it difficult to come to that decision?
Well, whether you realize it or not, you too are someone in need of forgiveness.
Every time we sin, we are that person who harms Jesus. We are the mockers who spit on Him, the soldiers who pressed thorns into His head, whipped Him, and drove nails through His hands. Our sin is the very reason He went to the cross.
And yet, He went willingly.
Knowing every sin we would ever commit, Jesus chose the cross anyway. He chose to suffer for the very people who sinned against Him. He chose to pay the price for the very people who deserved it. He chose forgiveness.
That's what makes Acts 10:43 so powerful.
Through His name, we receive forgiveness. Through His sacrifice, we are redeemed. Through His death and resurrection, a way was made for us to be reconciled to the Father.
The cross was the price of our forgiveness, and He paid it in full. 
You are a sinner, and Jesus saved you.