What does Y-axis of Normal Distribution's plot denote? As we know that in case of the continuous random variable, the probability of observing a single point (say x) is zero. But at the same time, we have the formula for N(mean, var) where N denotes a normal distribution. But if I put x in N(mean, var), I will get a non-zero value. Doesn't Y-axis of the curve corresponding to N(mean, var) denotes the probability?
 A: Not restricted to normal random variables, $p_X(x)$ represents the density value, which can be thought of as a relative measure that the random variable equals $x$. It is relative since it can be compared to other values in the domain, but it is not an absolute measure of probability since being equal to any specific value has probability $0$. In some analyses, this specific probability can be written as $P(X=x)=p_X(x)dx$.
A: I think the confusion comes from the following  - In a histogram the x axis shows the possible outcomes and the y axis shows the number of times each x outcome was observed. If there are N observations in total then dividing each number on the Y axis by N will give you the observed probability that each outcome happened so the histogram can also graph the probability of each x outcome.
Now when we have a continuous distribution the y axis no longer shows a count or a probability. Why not? Well, in a continuous distribution the literal probability that any particular outcome is observed is zero! This seems odd but just remember there are an infinite number of points between 0 and 1 or 1/2 and 1 or 3/4 and 1 etc. so the probability that any individual pt. happens is zero.
Even though the probability of any pt. is zero the probability of observing something within a range is well defined. e.g. if there is an equal probability of observing something between 0 and 1 then the probability of any specific pt. happening is 0 but the probability of a number between 3/4 and 1 happening is 1/4.
Now to answer your question, the normal distribution is defined so that when you integrate or sum the area under the normal distribution between any two points it gives you a probability
