'Insufficient Privileges' error displayed on a page you have permissions for

Root Cause
This error occurs when a user opens a Visualforce page containing a form tag in one browser tab, then opens a second browser tab and logs into Salesforce again (creating a new session), and then returns to the original tab and submits the form. The new login invalidates the session token associated with the original tab, causing Salesforce to reject the form submission with an Insufficient Privileges error.
This behavior was introduced in the Spring '16 release as part of a security enhancement.

How to Avoid This Error
Users can have as many Salesforce tabs open as they like, but they should avoid logging into Salesforce each time they open a new browser tab. Instead, open new tabs while already logged in — the existing session will be shared automatically. If the error occurs, refreshing the page in the browser resolves it immediately.