If you have a Facebook page for your business, connecting this adds a Shop to that page with all your items.
Xero is an online accounting system (see xero.com). When connected, ezimerchant automatically sends orders to Xero as draft invoices, making accounting for online sales much easier than alternative methods.
If you have a Google account (Gmail or Google Apps) you have Google Contacts. Connecting it to ezimerchant automatically synchronises your customer list in ezimerchant into an ezimerchant folder in Google Contacts. This can be used for marketing campaigns using third party marketing systems, which also support Google Contacts (many do).
Used for tracking website visitor data. If you don't already have a Google Analytics account you should set one up at google.com/analytics
Google Webmaster Tools
Connect to Google Webmaster Tools to monitor the health of your site
Google Product Search
Used in conjunction with Google Adwords to advertise your products on Google.