A call option is an option that gives the holder the right to buy the underlying security.
A call option can simply be a way of speculating on a rise in the price of security. It may also be used to hedge a short position. Hedging may be simple (call options over exactly the number of shares held short) to protect the downside, but a dynamic strategy provides a cheaper hedge that also hedges the upside (which may or may not be wanted).
The construction of dynamic hedges is used to value options, as the value of an option is equal to that of a portfolio which perfectly hedges it (and vice-versa). This provides the basis for deriving the Black-Scholes model.
As with all options, there are many types of call option such as American, European and various exotics and a wide variety of strategies in which these are used.