How is the E(X) of a Poisson distribution lambda?
The probability mass function for a Poisson-distributed random variable $X$ is $f_X(x)=\dfrac{\lambda^xe^{-\lambda}}{x!}$. The expected value is a sum over all possible values of $x$, the natural numbers (non-negative integers).

$$\mathbb{E}[X]=\sum_{x=0}^{\infty} x f_X(x)$$

When you evaluate that sum, the result is $\lambda$.

Yes, $\lambda$ often means a wavelength in physics. That’s just notation, however, and easily could be $\xi$ or $\beta$ or $\gamma$. Your physics knowledge will also tell you that $\theta$ is an angle, yet statisticians often use $\theta$ as a parameter. For the Poisson distribution, $\lambda$ denotes a rate, and this is how you get five cars per hour as the average rate of cars passing through a remote intersection (or whatever they’re doing).

EDIT

I like JBStatistics. He derives the expected value of a Poisson distribution, if you’re interested in seeing how that series calculation works: https://youtube.com/watch?v=65n_v92JZeE.