"Be ye not
'Unequally Yoked'

together with unbelievers", means,
Do not develop your closest relationships with people who are
not believers.  (This would include
dating, marriage, best friends,
business partners, etc.)
(The word 'yoked' used in this
verse comes from a Greek
word meaning: a chain,
a link, a bond,
a connection.) 
Be ye not unequally yoked together
with unbelievers:
for what fellowship hath
righteousness with unrighteousness?
and what communion
hath light with darkness?

2 Corinthians 6:14
In the olden days of America,
and still today in undeveloped countries, two oxen or other beasts of  burden, were 'yoked' together, at the necks,
with a large, heavy, wooden yoke, to form a team capable of working together to pull a plow or haul logs, etc.  These oxen had to be 'equally yoked'; in other words, be of the same size, strength and ability.  If a large, strong ox  were yoked with a small weak ox, the team would work poorly together, with the weaker ox being unable to pull
its load, perhaps tripping or even falling, thereby
causing the stronger ox to stumble or fall as
well.  In just this way, the very close or
intimate relationship between a
believer and unbeliever is a
dangerous and
unworkable
one. 
Can you think of any examples of how being"unequally yoked with unbelievers" could cause us to stumble and fall from
our Christian walk?