Start by running the Windows Store Apps troubleshooter.
Open Start > Settings > Update & security > Troubleshoot
Scroll down to the bottom
Click Windows Store Apps
Click Run the troubleshooter
When complete try opening the Store again.
Also check if the Store works in another user account.
Press Windows key + R
Type: wsreset.exe
Hit Enter
Do this a couple times then try launching the Store again.
Your Antivirus might be interfering with the Store, try disabling it 'temporarily' to see if it launches.
Check Windows Update and install the latest updates. Sometimes Microsoft releases infrastructure fixes for the Store through Windows Update.
You can also try resetting the store app using the following instructions: