My IP is 10.66.0.0 Subnet mask 255.255.0.0... what is my subnet? Is it 10.66.0.0/16 ?

Yes.

Additional Resources:
Wikipedia: Subnetwork (http://en.wikipedia.org/wiki/Subnetwork)
Cisco Systems: IP Addressing and Subnetting for New Users (http://www.cisco.com/en/US/tech/tk365/technologies_tech_note09186a00800a67f5.shtml)
Solarwind's Subnet Calculator (http://www.solarwinds.com/products/freetools/free_subnet_calculator.aspx)
Online IP Subnet Calculator (http://www.subnet-calculator.com/)

Yes your 10.66 portion is referring to your network and the 0.0 referring to your hosts.

A subnet is a 32-bit address used to identify portions of a network subnet/host.

The links above explain what it is, what it's used for and how to calculate!