The conventional boiler is simpler than a combi.
The boiler has a store of water which it heats up and a pump sends it round the radiators. It is the same water, it does not get used up, it just circulates round.
It is also sent to the cylinder, where it does not mix with the tapwater, but passes through a copper pipe coiled round inside the cylinder and immersed in the tapwater, heat passes from this coil into the hot tapwater in the cylinder.
There is a room thermostat on a wall somewhere that detects the rooms are cold and tells the pump and valve to send heat to the radiators, and a cylinder thermostat that detects the cylinder is cold and tells the pump and valve to send heat to the cylinder. There will be a timer or programmer that tells it what hours you want to heat the house.
For the hot tapwater, it is somewhat more economical to run the boiler for an hour or so morning and evening to fully heat the cylinder, than to let it run for a few minutes every time you run a hot tap, so there is (should be) a timer to allow you to set the timings. Once the cylinder is hot, it contains enough hot water to last all day, but it will be used up if you run a bath, hence time it to be replenished morning and evening. You can set it on all day if you want, the thermostat means that it will still only use gas when it needs to heat the cylinder. The cylinder will keep the airing cupboard warm and dry (if the door is shut) and is a good plafe to out your towels, sheets etc after washing and drying. It is not a drying cabinet so don't put wet stuff in there or it will go mouldy.
It will be capable of filling a hot bath faster than a combi, because the water has been pre-heated, but it is at lower pressure so showers will be weak.
There will probably be an electric immersion heater in the cylinder as well, but leave this turned off unless your boiler breaks down, because energy from electricity is about four times as expensive as energy from gas.
Is it a rented house?
What colour is the cylinder? This is important.