Not just sexual fidelity, but presentness. The covenant says: I will choose your good even when it is inconvenient. I will repair after a fight. I will not keep score.
In religious contexts, a covenant is far more than a simple contract. While a contract is a transaction of goods or services, a covenant is a bond of kinship. It establishes a "family" relationship between God and humanity, often sealed with an oath, a sign, or a sacrifice.
That word is
Whether you look at a marriage covenant (vows "for better or worse"), a blood covenant in a thriller, or the divine promise of salvation, the power remains the same. removes the option of walking away the moment the terms become inconvenient.