What exactly does "trustless" mean in terms of Bitcoin? People often say that Bitcoin is trustless, what exactly does it mean?

I know you don't need to trust one of following entities when you transact in Bitcoin, but what don't you need to trust?


third party 
recipient
other


You definitely need to trust Bitcoin system, right?
Bitcoin is untrusted, in that you don't need to trust a third party to use Bitcoin. Bitcoins are signed over directly from you to the recipient. This is binary, either the bitcoins remain under your control, or they have been signed over to the recipient. You can observe the state of your payment by running a full node, i.e. a Bitcoin client that enforces all rules of Bitcoin independently on the data it received from the Bitcoin network.

As you've suspected, you still trust the software that you're running, the community to continue operating Bitcoin under the same rules, and your recipient not to try to swindle you.

Each of those can also be mitigated to some degree, i.e. 


you can review open-source software yourself (or pay someone to do it for you)
you are part of the Bitcoin community that maintains the rules of Bitcoin
if the recipient sent you a bill that specified the amount and the recipient's address, you can prove a confirmed payment by means of the blockchain even if the recipient denies receiving it.