MapPress uses ‘dynamic’ maps (those are the ones you can pan and zoom).
Google is requiring everyone to enter billing info. Whether or not they actually bill you depends on your usage – probably most blogs will not pay anything, and I believe you can also set usage limits to prevent surprise billing.
You can learn more here:
If you think you’ll be paying for Google, you can try the latest (BETA) version of MapPress, 2.49. It supports Leaflet / Open Street Map maps, which are free, and MapBox maps which have a much higher free usage limit than Google.