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I was reading this article in wikipedia:

Suppose a species of bacteria typically lives 4 to 6 hours. What is the probability that a bacterium lives exactly 5 hours? The answer is 0%. A lot of bacteria live for approximately 5 hours, but there is no chance that any given bacterium dies at exactly 5.0000000000... hours.

Instead we might ask: What is the probability that the bacterium dies between 5 hours and 5.01 hours? Let's say the answer is 0.02 (i.e., 2%). Next: What is the probability that the bacterium dies between 5 hours and 5.001 hours? The answer is probably around 0.002, since this is 1/10th of the previous interval. The probability that the bacterium dies between 5 hours and 5.0001 hours is probably about 0.0002, and so on.

In these three examples, the ratio (probability of dying during an interval) / (duration of the interval) is approximately constant, and equal to 2 per hour (or 2 hour−1). For example, there is 0.02 probability of dying in the 0.01-hour interval between 5 and 5.01 hours, and (0.02 probability / 0.01 hours) = 2 hour−1. This quantity 2 hour−1 is called the probability density for dying at around 5 hours.

What does the 2 per hour mean? that 2 bacterias die in 1 hour? I am trying to understand what that ratio means

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If we refer to the probability measure for a continuous random variable to occur in an interval, as a probability mass, then the derivative at a point in the interval is named by analogy as the probability density.

It is the rate of change of the cumulative distribution function relative to the random variable, evaluated at that specific point.

$$\left.\dfrac{\mathrm d \mathsf P(X\leqslant x)}{\mathrm d x\qquad\quad\;}\right\rvert_{x=5\mathrm{hour}}=2\mathrm{hour}^{-1} \qquad=\lim\limits_{x\mapsto 0} \frac{\mathsf P(x < X\leqslant x+\Delta x)}{\Delta x}$$

So for intervals near enough to that time you can approximate the probability of a bacterium death occurring in that tiny interval.

$$\mathsf P(5\mathrm{hour}< X\leqslant 5.001\mathrm{hour})\approx 0.001\mathrm{hour}\cdot 2\mathrm{hour}^{-1}$$

This is an Intro. to Calculus level topic, is all.

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    ok, but for example lets take velocity. lets suppose velocity is 100meters per hour, if i keep this rate constant by an hour I wold have moved 100 meters. what I dont get is the meaning of those 2 per hour, of that were a constsnt rate, what it means, that after an hour 2 bacterias died? if so how i got from probability over an interval to that number? – 2017-02-10
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    It is just the change in *cumulative probability* of death at that time (it is not a constant rate), not in the bacteria themselves. – 2017-02-10