In Old Testament times, covenants were made in this way:
The two parties would cut an animal down the middle and lay the two halves down with a walkway between them.
The two parties would then walk between the two halves of the animal–showing their commitment and consent to be treated as the animal was should they break their part of the covenant.
When God made a covenant with Abraham, He passed through the animals by Himself. There was no way Abraham could keep his part of the covenant. He would have failed in no time.
When God passed through the animals by Himself, He took both the responsibility and the penalty should the covenant not be kept. When God saves a person, He takes full responsibility for him or her. He justifies and sanctifies. Nothing is left up to us to fulfill. How comforting this is!
It’s terrible that we’re so used to weak and pitiful depictions of God. God is not weak and pitiful. He is powerful and uses His power without consulting humans. He is One worth trusting. His love for His people lasts.
Note: Here is only my feeble attempt at retelling what I heard during a sermon. I have not extensively researched covenants myself.