Abbreviations are shortened forms of words. They were originally created back in the dusty, pre-computer days when everybody wrote things longhand. They saved writers time and probably prevented a lot of nasty hand cramps.
Today, we don't have as great a need for abbreviations in formal writing, but some hardy abbreviations or acronyms have managed to hang around. Check it out:
titles before and after people's names
Mr. Wendall; Gregory House, M.D.
time
6:45 p.m., 125 B.C.E.
familiar countries
U.S.A., U.K.
familiar objects
DVD, PS4
well-known corporations and organizations
CBS, IBM, NAACP
Latin terms (save these for your footnotes and parentheses, though)
i.e. (that is), et al. (and others), etc. (and so forth), e.g. (for example)
While we know your time is ultra valuable, don't go overboard with the abbreviations. The following things should not be abbreviated in your papers and essays (but can be in other situations):
measurements
write centimeters not cm.; write pound not lb.
days and months
write Friday not Fri.
place names
write New York City not N.Y.C.; write Avenue not Ave.
areas of study
write biology not bio.
chapters, volumes, and other parts of works
write chapter not ch.