This weird box keeps popping up on my homepage--

It says:

Allow this website to use additional space on your disk?

The website Google.comis requesting 10 MB of disk space to store (email address) as a database on your disk. Currently the website is allowed to use 5 MB of disk space.

Then one box to click DON'T ALLOW and ALLOW

What is this. I sure don't trust it? Like Google needs space on my Mac. Anyone else run into this?