why, out of all the other numbers, has 2 selected as a base number of binary?

2 is the "base" number for binary because each binary digit has only 2 states: 1 or 0. This is important to understanding computers because "bits" of storage also have two states, "on" and "off". The 1 and 0 of binary digits directly correlates to the on and off states of the bits.

In short it's because it's simpler to determine whether or not a signal is on or off (1 or 0) than whether it matches one of many states on a more granular scale.

Electricity varies a little as it passes through a circuit, we can say on is anything above x, and treat anything lower as off, even if there is some current passing through. If we tried to measure more precisely we might find that under certain conditions our measurements were wrong. We have absolutely mind boggling amounts of these on or off states put together to form modern computing, their accuracy behind the scenes is crucial and a binary system makes this base level accuracy easier to achieve.

It's important to understand how binary works because computers store data and execute instructions using binary. This might seem like something you don't really need to be aware of, but it actually has implications for how much space a string takes in memory. If you're dealing with a few paragraphs that's not big deal, if you're working for Wikipedia though how you encode, store, retrieve and display that text might be worth thinking about in terms of bytes and bits in binary.

That's probably not a great explanation, if you look more into transistors, semiconductors, and electronic circuitry you'll get a better understanding.