Dictionary.com

noun

• an agreement, usually formal, between two or more persons to do or not do something specified.
• Law. an incidental clause in such an agreement.
• Ecclesiastical. a solemn agreement between the members of a church to act together in harmony with the precepts of the gospel.

verb (used without object)

• to enter into a covenant.

verb (used with object)

• to promise by covenant; pledge.to stipulate.

Etymonline.com

c. 1300, covenaunt, “mutual compact to do or not do something, a contract,” from Old French covenant, convenant “agreement, pact, promise” (12c.), originally present participle of covenir “agree, meet,” from Latin convenire “come together, unite; be suitable, agree,” from com- “together” (see com-) + venire “to come,” from a suffixed form of PIE root *gwa- “to go, come.”

In law, “a promise made by deed” (late 14c.). Applied in Scripture to God’s arrangements with man as a translation of Latin testamentum, Greek diatheke, both rendering Hebrew berith (though testament also is used for the same word in different places). Meaning “solemn agreement between members of a church” is from 1630s; specifically those of the Scottish Presbyterians in 1638 and 1643 (see covenanter).

Discussion/Explanation

The above information is correct. It is a pact or a sort of promise if you will. However, in Old Testament Hebrew tradition, it went even further than that.

In the original Hebrew, the language used for making a covenant involved cutting. You were “cutting a covenant” agreement but the cutting analogy did not end there as it would turn red with blood too. An animal (or more) would be cut in two as a visual representation of the importance and severity that would result to the one who broke the covenant.

We think of covenants today as a sort of contract but in Old Testament times, they were a blood contract that demanded blood if you failed to keep it. This is an important component in Biblical Theology as man repeatedly could not keep the covenants made and paid the price.

Thankfully one day there was one who could keep them perfectly but instead of us paying the price, He did with His life which is why we now turn to Christ for salvation rather than anything/one else.

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