Answer: In the scripture you reference, Paul is using the analogy of animals unequally yoked or put together to make a point concerning our associations with other humans. The verse in question is in chapter 6 of 2Corinthians. Interesting, this is the only place in the KJV New Testament where the word yoked is used.
Do not be unequally yoked with unbelievers. For what do righteousness and lawlessness have in common? And what fellowship does light have with darkness? And what union does Christ have with Belial? Or what part does a believer have with an unbeliever? (2Corinthians 6:14 - 15, HBFV)
Paul is drawing his analogy from the Old Testament prohibition against yoking an ox with a donkey (Deuteronomy 22:10). Related to this verse is Leviticus 19:19 that warns of breeding differing kinds of livestock.
Animals that were placed together had a piece of wood used to connect them, each with their own collar, so that their combined abilities could more easily perform a particular task. Oxen, horses, donkeys, and mules paired in this fashion were good for pulling a load, plowing a field and so on. Farmers knew that it was not wise to unequally couple animals together.
Animals were also yoked together as a teaching device. A seasoned animal would be connected with an untrained one. If the untrained one lagged behind, the seasoned animal would keep up the proper pace, and the trainee had no choice but to keep up. If the trainee decided to go to the left or right, the seasoned animal controlled that as well.
The context of Paul's admonition is the relationship of believers (Christians) with unbelievers. Its most obvious application would be within the confines of marriage.
Matrimony is, in a way, an agreement a man and a woman make to be yoked together in order to make their journey through life a bit easier to bear. Between them, they must bear the 'load' of maintaining a home, rearing children and so on.
As a general principle, it is not a good idea for a Christian to be yoked (married) to a non-Christian. The beliefs and practices of a true Christian could easily be considered a constant irritant to the unbelieving spouse and thus strain the relationship. Furthermore, the habits and behavior of the unbelieving spouse, over time, could have a negative impact on the believer.
Paul's teaching could also be applied to business relationships. It would be wise for a Christian to consider a business partnership that would tie themselves to someone who is unconverted. Such partnerships could lend itself to a believer compromising his conscience or otherwise going against Biblical standards of integrity, honesty and generosity. Choosing to be unequally tied with someone who has a different standard of behavior is a risk that could ultimately prove costly.
Jesus tells us that we can avoid or lessen being unequally yoked together if we ". . . learn from me; for I am meek and lowly in heart; and you shall find rest for your souls" (Matthew 11:29, HBFV).