what allows some cold water to enter house and some to enter water heater?
I know I am going to be a bit long winded at first before making the point - for a reason so hang on.

Well consider the entire system as a closed system nothing is flowing anywhere at all. When these systems are put together there is also no water at all in the lines so when a valve is opened the water is allowed to flow into the lines or not so much because there is air in those lines. So when the home plumbing is newly turned on at a faucet for example the air is forced out of the lines and you can see this happening. With the water heater the same event must occur - you open a hot water faucet and the water can then flow - previously all of that air pressure kept it back to some extent. Now all of that air is forced out of the water heater and the plumbing lines until you have a system that is filled with  water only.

So now the pressure at any given point is kept in the system by the closed faucet. When you open the facet the water will flow (because it is pressurized by the city) , so that water flows at a certain pressure rating (USA about 80PSi is normal for a residential household). 

When you open the hot water faucet you have removed the resistance to the flow of water , because of the pressure of the water and the lack of resistance to it's flow via the hot water tank and the house pipes the water can now flow freely through the path of least resistance - your hot water system.

Now all of that said here is another bit that I know you did not ask for but think can add some real value to your question. 

Remember I said when the system was new how all of that air was in the lines , well the same thing will happen when a water heater is replaced - Air will be in it. With a new hot water heater the air must be purged from the system (displaced by water) before you turn the hot water heater on or you will burn up your brand new water heater. This is why it is very important to purge the lines of air after replacing a water heater.