If you own a windows phone 8.1 device, you are likely eligible for an update to windows 10 mobile. To fetch the windows 10 update, you will have to install an app called upgrade advisor from Microsoft Store. This is because Microsoft did not push the windows 10 update automatically and wanted users to enable the upgrade themselves.
This is totally unlike laptops and ultrabooks that got the upgrades automatically on their devices. No ultrabook or laptop had to install any kind of upgrade advisor to upgrade from windows 8.1 to windows 10. The update was pushed through windows update to all users and that is why all the laptops and ultrabooks france and USA sold during windows 8.1 time were said to be compatible with windows 10. The laptop manufactures made sure that there were no compatibility issues between drivers of windows 8.1 and 10 in order to avoid any annoying issues. Windows 10 upgrade was made as seemless as possible on ultrabooks and laptops.
Anyway, back to windows phone. Once you have downloaded upgrade advisor from store, backup from device. For that, go to settings > backup and then follow the instructions on the screen. Make sure you have enough free storage space on your phone. You will need around 3GB-3.5GB free on the phone for the update to install.
Then fire up the upgrade advisor app and select the windows 10 update. It will ask you to restart the phone. After restart, make sure you are connected to Wi-Fi as your phone should now start downloading the update. If it does not, go to Settings > Phone update and check for updates. The windows 10 update should now be downloading. Feel free to use your phone as the update downloads in background.
After it has been downloaded, your windows phone will ask you to install it. Get a coffee or something as that will take around 30-40 minutes to install.