The aim of Tor is to improve your privacy by sending your traffic through a series of proxies. Your communication is encrypted in multiple layers and routed via multiple hops through the Tor network to the final receiver. Note that all your local ISP can observe now is that you are communicating with Tor nodes. Similarly, servers in the Internet just see that they are being contacted by Tor nodes.
Generally speaking, Tor aims to solve three privacy problems:
First, Tor prevents websites and other services from learning your location, which they can use to build databases about your habits and interests. With Tor, your Internet connections don't give you away by default -- now you can have the ability to choose, for each connection, how much information to reveal.
Second, Tor prevents people watching your traffic locally (such as your ISP) from learning what information you're fetching and where you're fetching it from. It also stops them from deciding what you're allowed to learn and publish -- if you can get to any part of the Tor network, you can reach any site on the Internet.
Third, Tor routes your connection through more than one Tor relay so no single relay can learn what you're up to. Because these relays are run by different individuals or organizations, distributing trust provides more security than the old one hop proxy approach.