There is nothing built into Store that would allow actual address verification if you are using the default shipping plugin. Third party plugins USPS, UPS, FedEx offer some verification between City, State, & Zip but won't stop a user from checking out in most cases.
If you do not offer free shipping on your site you could easily prevent the user from being able to checkout by making sure the shipping total is higher then 0.
{exp:store:checkout ...}
... other template code ...
{if order_shipping_total > 0}
<input type="submit" value"submit" name="submit" />
{else}
Something appears to be wrong with your shipping details please make sure everything is valid
<input type="submit" name="update_cart" value="Update Cart" />
{/if}
{/exp:store:checkout}
There are multiple address verification APIs that you could also integrate yourself. I personally use SmartyStreets on a few of my clients sites but there are many other too. EasyPost is very nice and also allows you to print shipping labels and connect to many other shipping providers (would require a custom shipping extension), PostCoder Web, USPS, UPS, StrikeIron World, or StrikeIron NA just to name a few.