Some exotic options are said to be path dependent. Their terminal value (at exercise or expiration) depends upon the value of the underlier, not only at that time, but also at prior points in time. In this sense, the option's terminal value depends upon the "path" take by the underlier over the life of the option.
A call option is not path dependent. Its value at exercise or expiration depends on the value of the underlier only at that point in time..
By comparison, an Asian option is path dependent. Its value at expiration depends on the average value of the underlier over the life of the option. A barrier option is also path dependent. The option's value at expiration depends upon both the value of the underlier at expiration but also on whether past values of the underlier ever hit a barrier. Chooser and Lookback options are also path dependent.
Pricing or calculating the Greeks is typically more difficult for path dependent options than for non-path dependent options.