Adding TOR gives you a lot of added protection to some threats, but it's not perfect.
Assume you log in to a web site through a valid TOR network with a valid TOR client.
Also assume your computer isn't compromised. (i.e. no spyware on your computer.)
Data goes through multiple computers, referred to as relays or nodes.
Your traffic (data) is encrypted by your computer and goes to an input relay. That relay node re-encrypts the data and passes the data to another "intermediate" relay. I think TOR sends the data through at least two intermediate relays. The last intermediate relay encrypts the data and sends it to an "exit" relay or TOR exit node.
The last exit node sends the data unencrypted to the web site.
When the exit node responds and sends data back, it sends unencrypted data back to the exit node, and it encrypts it and forwards it back through the same chain.
If you log into www.bob.com through TOR, the data between the exit node and www.bob.com is visible and readable to anyone just as if you connected to www.bob.com directly.
Anyone snooping at www.bob.com, the TOR exit node, or anywhere between those two nodes can see all your traffic. However, they cannot see your originating IP address.
Anyone snooping on your network, on any of the TOR relays other than the exit node, or any of the network cannot see your data or that coming back from the web site. They cannot see which web site you are connecting to.
Note that the link between the last node and the web site is in the clear and can be read by anyone who can see that data. The way to fix this is for the web site to support https. This encrypts all traffic on top of what TOR does. https prevents snooping on the last link in the chain and keeps anyone from snooping unless they have access to the internals of the computers at www.bob.com.
There are some potential weaknesses in the above system.
There could be some sort of hidden malicious code built into the TOR system.
There could be some sort of flaw, either malicious or accidental, in the code.
There could be a weakness, either malicious or accidental, in the math for the encryption used.
There are some more esoteric ways to attack a TOR connection, but they usually require quite a bit of resources on the part of the attacker.
Probably the biggest risk is a rogue TOR exit node. If the TOR exit node is compromised, it can see all your web browsing just like a wiretap at the web site's ISP can. That's why https is so important.