When you turn on the cold water tap in your home, you expect it to come out cold. Unfortunately, for some homes, this is not always the case. It could be that when you turn on the faucet the water comes out warm to start with and then it gets cold after running for a while. It is also possible that the water comes out cold first and then turns warm.
How this happens depends on where the problem lies.
If you have uninsulated pipes running through an area of your home where it gets very hot, such as a garage or an attic, the water might get heated up while sitting there, hence the hot water right away when you open your faucet.
On the other hand, if you have a malfunction in your water heater where the hot water makes it into your cold water pipes, you would see the second scenario with the water turning warm after running for a while. There are also other reasons why you might have these problems, so it might be a good idea to have a plumber take a look at your system.