Calculus is a branch of mathematics, and a rather important and fundamental one. It was created by several people but Issac Newton is the one that is given credit for it. Calculus can be used to explain a rate of change (derivative) or area under a function (integral). it also bleeds into differential equations, has major applications in engineering and science in general.
it comes from Latin which means small stone used in reckoning. in calculus you deal with small increment (infinitely small) stones also have a history of being used in calculations.
EDIT: in engineering (the area i study, particularly electrical) it is used to find how much work or energy you must do to do some thing. it is used to analyze electronic circuits and the signals going to them. it allows you to find an average of a continuous function... it can be used to model transformers, capacitors, and inductors.
it is used in physics a lot, particularly modern physics for "normalizing wave functions" which helps tell you where an electron may be in a given area. it is also used in statistics for analyzing the probability of something on a bell curve.
in all honesty now that i know calculus, i cant image a word without it, its worthwhile to learn if you need to, but it also may cause you a head ache trying to learn it.