The W-9 is used for anyone with a tax ID number (SSN or ITIN) and basically says, “Hey IRS/Treasury, this is my Tax ID number”.
Many banks are now requesting this document because of FATCA reporting requirements – since they have to report the assets of their American customers to the US, the W-9 or W-8 (in rare cases) is best suited for that.
I will mention that even though the W-9 is just a reporting document (you are not taxed on anything), if you are not caught up on your US filing regulations (Tax returns and FBAR's), it could be bad news. It is much better to voluntarily be up to date on your tax requirement, and to tell the IRS yourself (with your yearly tax return), then to have your bank "tattle" on you.
Lastly, the W-8 series is used to certify that the you are not an American citizen or American resident. Even though there are many of these, it doesn't sound like it would apply to your situation (they’re more used by nonresidents with US-sourced income).
I would recommend getting caught up on your US filing as soon as possible. It is better to be safe than sorry in my opinion.