Well, sometimes using the physical "Power button" to shut down doesn't actually turn it off. It may well be putting the system into standby mode.
There are two ways to fix this.
1. To turn off the laptop you can click the "Start button" (mouse over the arrow at the bottom-right corner of the Start menu) and then click "Shut Down".
If you have been clicking the little "power-button" icon to the right of the search box to turn it off, the problem with that is the default Windows setting for that is the same as for your physical power button: standby.
2. You can actually go in and change the function of the power button (and the onscreen power button) so that it does actually Windows, rather than putting it into standby.
Sadly someone somewhere decided that pushing the power button on a laptop should go into standby, rather than turn it off.
The following will help you change the setting.
Go to "Control Panel" and then "Power Options".
Click on "Change plan settings", next to the plan you are using.
Now click "Change advanced power settings".
Scroll down and locate "Power buttons and lid.
Click the "plus" to open that and then click "Power button action".
Click the blue work/link next to "Setting:" and change "Shut down", if you want to use the power button to turn the laptop off.
Now click "Apply" and then finally click "OK".
Your power button, and the one on the screen, should now turn the computer off.