saty.satya,
In a linear phase filter, the phase shift is directly proportional to (is a linear function of) frequency. Linear phase is important in applications where the waveform of a signal must be preserved. If you don't have linear phase, then the waveform of any signal other than a sinusoid will be distorted. A linear phase filter behaves like a pure delay.
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A word of caution regarding FIR filters; They are not necessary linear phase. You can achieve linear phase only by observing certain rules regarding the symmetry of the coefficients. For example, with an odd number of taps, if the coefficient values are symmetrical with respect to the center coefficient, then the filter will have a linear phase characteristic.
Regards,
Kral