Google provides three different editions for organizations: Standard, Educational, and Premium. Standard and Educational are free. Premium runs at $50 per user account per year.

Standard: This contains the Google products you're already familiar with: Gmail, GCal, Google Sites, Google Docs, Google Talk, and a Google Start page. These products function the same as their consumer counterparts, but Google Apps provides an administrator control panel for creating users and managing their accounts. Administrators can reset passwords, create default security settings, and limit sharing of organization documents outside their organization. 

Even this most basic version of Google Apps can be integrated with a new or existing domain (e.g. http://www.yourorganization.org) - making it a great option for small nonprofits operating on a tiny budget.

Education (Nonprofit): Although officially targeted at schools, the Education edition of Google Apps offers a full suite of office productivity applications at an unbeatable price. For organizations using an email server, the Educational edition gives you access to extra email, calendar, and site features. It also provides a useful email migration tool for moving existing email from your mail server to Google Apps at designated intervals so they do not overwhelm your IT infrastructure. For calendars, Google provides conference room and resource scheduling. Also, you receive the same support as premium users with 24/7 assistance and phone support for critical issues.

Premium: This Google offering has everything the Educational version has, but with some nice additions. Email storage is raised to 25 GB. There is a policy management system that lets administrators track messages, route them for review, or block if desired. More details can be found here. Support is the same as that given to nonprofits and educational institutions, but this is the alternative for anyone without 501(c)(3) status from the IRS.