A channel is Public by default. Anyone can notice a public channel, see its users and join the conversation. In a list of channels you can see a public channel's topic. When someone is on a public channel, he can be easily found by all other users as long as his personal user mode is not set to invisible (see below).
An Invite-only channel can only be joined if you are invited by one of its channel operators.
Private channels turn up normally in the channels list. People can see you are on a private channel somewhere, but they can never find out on -which- private channel you are unless they search all (private) channels by brute force. With the names command your nickname will not show up, but it will with the /who channel_name command unless you hide by setting your personal user mode to 'invisible'.
Secret channels do not show up in a channels list and you cannot find out its topic unless you join it. If you are on a secret channel, someone who is not on the same channel can't see that you are there, regardless what your personal user mode is set to. Your name does not show up in a names list of people on IRC if you are on secret channels only.
Your User mode can be set to Invisible meaning that other people cannot find you by searching on IRC unless they know your exact nickname. No (wildcarded) search on you by the /who command on your IP Address or real name will deliver your current nickname or other likewise info to others.
When your user mode is restricted you do not have the power normal channel operator have on channels (you cant use /mode, /kick, ..etc.) and you can not change nickname (/nick). But you can chat normally.
