I have always wondered why when signing up for websites or apps, some companies would send out an email for verification, but would give the users complete access to the app/website anyways. What would happen if the user never clicks the verification link in their email?
This depends entirely on the site.
Sometimes they're merely validating your email address. They're fine if you use the site, but they might keep bugging you with an alert if they never get a response to the email confirmation.
Other times, they are letting you in as a courtesy...so you can immediately use the site, but if you don't validate your email, they may lock you out after a short period of time.
Often it is only the first time that you can log in without verification. So you will eventually need to verify after all.