The significance of walking through the animal pieces to ratify the covenant was that the covenant parties bound themselves to the covenant terms under penalty of being killed as the covenant victim was if they broke the covenant. In other words, if they didn't fulfill their obligations to the covenant they would be killed as the animal(s) was. It was a very solemn vow; nothing like it exists in our time
This is observable in the blood covenant made with Israel at Mt Sinal (Mt Horeb). As soon as they broke the covenant, God intended to destroy them, which would have been the just response. But Moses interceded on their behalf and God spared them because he is merciful.
And the LORD said unto Moses, I have seen this people, and, behold, it is a stiffnecked people: Now therefore let me alone, that my wrath may wax hot against them, and that I may consume them: and I will make of thee a great nation. Exodus 32:9-11
Nevertheless that covenant was broken and no longer in force. That is why God made another covenant with Israel in Moab (Deuteronomy 29:1)