What does the $\prod$ symbol mean?

This is one of those cases where I would google if I could, but I don't know what to search for.

I've come across this symbol a few times, but I have no clue what it means or what it is called.

$$\prod$$

Furthermore, what are the $\coprod$ and $\amalg$ symbols for?

I could not list all the places I found it, but the one that sparked it was a discussion on solving the Diophantine equation, $\frac{1}{x} + \frac{1}{y} = \frac{1}{n}$.

The symbol $\Pi$ is the pi-product. It is like the summation symbol $\sum$ but rather than addition its operation is multiplication. For example, $$ \prod_{i=1}^5i=1\cdot2\cdot3\cdot4\cdot5=120 $$ The other symbol is the coproduct.

The uppercase Pi $\prod$ symbol stands for the $product$ operator throughout mathematics, just as the uppercase Sigma $\sum$ symbol would describe the sum operator. Think of the following analogy alliteration:

Pi is to a Product ... as Sigma is to a Sum.

For example, $$\prod _{i=0}^{3}a_i=a_0\cdot a_1\cdot a_2\cdot a_3$$

This is a symbol for product similarly as $\sum$ for sum.