Hi BoSChoW
I'm not sure how basic we need to start in order to answer this question. I know from previous threads that you've been working with digital or discrete data points - on or off. Analogues are quantities which vary in accordance with some physical quantity. Flow rate, temperature, pressure etc are all physical quantities. Specialised devices referred to in general as sensors detect these quantities and convert them to an electrical signal which is analogous to the physical property - hence analogue. The higher the flow rate, temperature, pressure etc the larger the electrical signal.
There are common industry conventions for these electrical signals. Some sensors produce signals in the range 0-10V DC, some produce 0-20mA or 4-20mA. So a 4-20mA temperature sensor which covers the range -20 deg to 200 deg will produce 4mA at -20 deg and 20mA at 200 deg. Exactly half-way, 90 deg, will produce 12mA and so on. There's a whole industry dedicated to the design and manufacture of more types of sensors than you can imagine.
The PLC analogue input then receives this electrical signal and converts it to a numerical value within the CPU's register. Different models of PLC will use slightly different ranges, but for example Siemens S7 uses a fixed range of 0 - 27648 to represent the incoming 4-20mA (or other) signal. Our half-way value of 90 deg would be represented as 13824. Of course you can perform arithmetic to scale this integer as a floating point value so you are actually using a value in the PLC of 90.0 If all you want to do is monitor or detect certain ranges then you can just compare your incoming value against known setpoints.
With analogue outputs, the reverse happens. You calculate a value in the PLC which represents perhaps a valve position, say 75% open. Well, 75% of a scale of 0-27648 is 20736 so you write that value to the output address. The output module then converts that value to another standard electrical signal and delivers it to the actuator attached to the valve. It is designed to move the valve according to the voltage or current it sees and so you can control the valve position. If your valve is controlling the flow of steam or hot water this may be tied to your temperature sensor and so you will find a change may happen in the analogue input.
And now you have a control loop. But that's a whole other story and many other threads...!
Regards
Ken