All of mankind, every last one of us, are sinners. We all fall short of our best, no matter what our best is. God The Father knew this when He created us, but He also knew that we needed the chance to be born on earth and have the experience of mortal life. At the same time, no unclean thing can dwell in the presence of God, and we needed some way to become clean despite our inevitable sins.
The Father created a plan for a Savior to sacrifice for all of us, so that we may all have the opportunity to repent of our sins. The Book of Mormon teaches that this Savior's sacrifice needed to be a "great and last sacrifice," and that it must also be "infinite and eternal." Jesus, The Son, then volunteered to come to earth and be the Savior called for in God's plan, which we call the Plan of Salvation or the Plan of Happiness. He offered Himself as the infinite and eternal sacrifice.
In what ways was His sacrifice infinite and eternal? If one is going to pay for the sins of all of humanity that has ever lived, every last one of our sins, then the sacrifice must be infinite to be able to cover everyone; it must be eternal in order to span all of humanity's existence.
He was the Son of God. The Savior was born of Mary, but His father is The Father of us all. As such, He was not subject to death as the rest of us are. He has power over death, just as He has power over nature, sickness, and really all things. He is eternal, and therefore His sacrifice is eternal.
Before anaesthesia worked as well as it does today, it was common practice to restrain the patient for painful procedures. Most of us cannot prevent ourselves from fighting back against pain, even if we know we need the operation done. What bands could've held our Lord's power for Him to submit to whipping, scorn, and utter humiliation? Even worse, to suffer all this at the hands of pathetic men revelling in the power of ruling a subdued nation. His sacrifice was infinite in humility: He had power over every soldier and ruler and could've exercized it as easily as over the fig tree, yet He chose to submit.
He was perfect. He never fell short in any way. This is almost incomprehensible. Of all of the things we do every day, how many can we do perfectly? I think I'm now perfect at getting my right shoe on my right foot. I think I'm really good at washing my hands, but I don't think I'm 100% perfect at it. Our Savior lived a perfect life. I've never lived a perfect day. His sacrifice was infinite and eternal because He was completely innocent and He was sacrificed for us, the guilty. The only man ever to achieve mind-bogglingly impossible perfection willingly suffered and died for us, despite the fact that we do not deserve it.
I do not understand how our Savior paid for all of our sins. I don't understand how it is possible for Him to take upon Himself all of our guilt and also all of our pains and sufferings. I cannot comprehend how He can do this for me, let alone for everyone. However, I know that it is true. I know that He bridges the infinite gap between our sinful mortality and the eternal glory of God.