How electrical signals converted into Digital (binary 1 0)
Your question assumes that there are somehow two kinds of electricity, analog and digital. This is not the case. The difference between analog and digital is how we humans interpret an electrical signal. Electricity is electricity, it does not care how we interpret it. 

For an analog signal we interpret its level value (voltage, or sometimes current) as conveying information with infinite resolution: in the ideal world 1.00000 Volt and 1.00001 Volt convey different information (the latter could mean for instance that the measured temperature is 0.1 degree higher).

For a digital signal we interpret its level as conveying just one bit of information. For instance, below 2.5V (but ideally 0V) it conveys a 0, above 2.5V (ideally 5V) it conveys a 1. 

An analog signal can clearly convey much more information with just the level on one wire. A digital signal on the other hand has the very important property that a little noise on the line does not affect the information in an ideal signal: 0V (ideal 0 signal level) + 1V noise => 1V, which is still recognizable as a 0 level. This means that a digital signal can be transported, stored/retrieved and processed without loss of information. 

It turns out that it is much easier and cheaper to create a digital circuit that handle/store/transmit let's say 20 bits (which together can represent ~ 1*10^6 different values) than to create an analog circuit that can do things with an analog signal with an accuracy of 1*10-6. Hence the trend to do everything digital.

That brings us back to your question of A/D conversion. Our real world is inherently analog, and so are (nearly?) all our sensors that interface with the real world. They produce an analog signal, which we would like to feed into our digital circuits. The circuit that does this is called an Analog-to-Digital-Converter. IIRC there are good explanations on SE of the working of an ADC.