Syntax:

/mode nickname +/- mode(s) 

Contents:

User modes are commands that you can set by you to control what information others can see. Currently users can set themselves:
+/- i (invisible)
+x (host hiding)
+/- d (deaf to channel chat)
+/- w (get network broadcast messages)

User modes are set or un set via the + and - signs.
For example, to turn mode i (invisible) on, /mode +i. To turn the i mode off, /mode -i.
You can also turn on multiple modes at once, or turn some on and others off

/mode harry +di Turns on d and i modes for you if your nick is harry.
/mode johnny5 -d+i  Turns d mode off and turns i on.

+d  This is (d)eaf mode; you won't see any channel text at all. You will still see joins, parts, topic changes, kicks, bans and other channel mode changes.
You will only be "deaf" to channel chat. All other chat, via /msg, /query etc. will be seen by you the normal ways. Channel bots are often set +d (like the cservice bot X) and only respond to /msg.
If someone is usermode +d, then a /whois on them will show a "-" in front of the channels they are in. For example: 
*** nick is ident@username.users.undernet.org
*** on channels -@#userguide -#somechannel
*** nick using *.undernet.org The Undernet Underworld
*** nick End of /WHOIS list.

Note that going +d means being "deaf" in *every* channel you are in. You cannot be deaf on a per-channel basis.

+i  This is (i)nvisible mode, and to answer the obvious question, no, you can't be invisible inside a channel such that no-one else can see you. Suppose Banjo is +i and in channel #popsicle. Now suppose stoney` isn't in #popsicle, and does /names #popsicle to see who is inside the channel. Being +i, Banjo will not show up. Furthermore, suppose Banjo's /whois address is Banjo@ppp.ihug.co.nz. If stoney` types /who *ihug.co.nz to see who is on from the ihug host, Banjo will once again not show up. If stoney` IS in #popsicle, however, then icesmurf will show up in the /who output: 
Banjo is (Banjo@ppp.ihug.co.nz)
*** Banjo is < Banjo >
*** Banjo on *.undernet.org
*** Banjo on #popsicle
*** Banjo online since Sat Feb 08 231147 2003 

+x  This is host hiding usermode. This means it will hide your real IP/host and, instead, show ident@username.users.undernet.org. You will need to log in to X (have a username) to enable this mode. There's no way to turn off this mode other than disconnecting from the IRC and then re-connecting without having yourself +x. For more info on host hiding join #cservice.

+w  Wallops are network wide messages sent by IRC Operators. Any user who is set to +w will also be able to see the message. Messages are usualy about new features added to network, security, events.