probability density function of a continuous variable

Hello all,
I am new to this forum as well as the field of random variables. I read that, for a continuous random variable, the probability that the variable takes a particular value is zero, which was proved by using distribution function being continuous, so the left limit at a value equals the value at that point. But i was not able to interpret this result.... Won't the probability density function's value at that point give the probability for the ran var., to take that value? Plz help me out...