CRM in CiviCRM stands for "Constituent Relationship Management" and not "Customer Relationship Management".

CiviCRM offers "classical" CRM features:

• contact database (with as many emails/phone/adresses per contact as needed)
• relationship management (bob is the assistant of jane that works for acme that is a branch of acme holding)
• mass mailing/newsletters, automatic handling of bounces, personalisation "dear Jane", track click/open...
• tracking activities (phone calls/meetings...)
• reporting

It focuses on the not for profit sector, and provides extra components:

• Donations (including credit card processors integration)
• Event management, online registration
• Membership management
• Surveys/Petitions
• Case management (kind of project management, list of activities and actors, timeline...)

It integrates with several other modules: webform, organic groups, views being the most known.