DFU mode refers to Device Firmware Update. If a restore using Recovery Mode is not working or getting some errors on iTunes, you will require to use DFU Mode as a last option. When placing your iPhone into DFU Mode it does not load the OS before attempting the restore and this steps skip some errors to appear that validates previous iOS version on your iPhone, iPad or iPod.
Step 1. Open iTunes software on your PC / Mac
Step 2. Power of your iDevice and press power button for 3 seconds (You should be able to see Apple logo) and then keep power button pressed but also press home button and keep it pressed until screen goes black (the way old tv goes to sleep) and then release power (Sleep button) but keep your home button pressed for approx 15-20 seconds. Here is a reference image for sleep and home button. Keep in mind, sleep button is also known as Power Button or lock Button
Step 3. Once you get DFU mode on device, iTunes will show you following message but there will be no sign or no display on iPhone. iPhone will look like completely switched off.
If required, process all steps again until you get DFU mode. Once you receive DFU mode confirmation, Connect with iTunes and update your iOS.
Generally It can take more than few attempts to gain DFU Mode, and in this process you often end up with recovery mode. Hold both home & sleep/power button for 10 seconds and then release only sleep button but keep pressed home button. It will get your iPhone DFU mode a lot faster.