You asked what the connections are:
the first poster answered that as well as I could, they are the connections to and fromyour box, the last column is the state of the "socket" (connection). these are FASCINATING things, and it always pays to know about them, Sys Admin did an excellent article this last year on socket states, look it up at their site,
www.sysadminmag.com, I think
You also asked about knowing what the ports are doing:
again, the other posters covered this extremely well, lsof and ps are your friends here, as well as teh iptraf command, do a man on any or all of them and if you don't have lsof, I suggest getting it, it is very useful. You could also turn on promiscuous (?) mode on your interface with tcpdump/etherpeek/snoop/any other packet dumper, and look to see what is coming in, that is an education in networking in itself. Do a man on tcpdump, and you can learn more about ip traffic than you thought existed.
You also asked if closing the ports will do any harm:
That depends, are you connected on the port via telnet to your remote machine? If so, it would kill that session, you could also kill mail, and many other helpful connections to your machine, not to mention any servers listening on ports (these will be in a state of LISTEN).
Now, some also mentioned that you have to wait for a length of time before you can see the port be released and may reuse it again. this is true, but it is also usually a kernel parm taht is settable and can be cranked down to 5 seconds (or less on some platforms), be CAREFUL with this, it is dangerous to set your timeouts so low.....
Noe there is also an interactive way to kill these ports and NOT wait, WITHOUT the kernel parm; Dugsong put out a tool a while back called dsniff, it is a suite of some really wicked tools he used to figure out some networking things on his own system. There are some amazing things in there. One of the tools is tcpkill, it allows you to kill a socket on the localhost and NOT timeout the port, it just goes AWAY... very good programming...
He has made this available in the *BSD ports and packages, as well as at his site, which is quite interesting (when he isn't censoring it due to the DMCA...
www.monkey.org/~dugsong/dsniff.html ought to get you there. I will warn you, this tool is very dangerous in the wrong hands, it was intended for learning and should be used with the respect due to it and it's author. Using it illegally would endanger eveyone else's access to it, not only your own, so think of others and use it wisely and respectfully... please.
Ciao
loadc