The Nick List is by default, on the right hand side of the screen. It displays a list of each person in the current channel. Below is an example:
As you can see, the channel name is on the bar at the top. Next to the channel name is the nick count (How many people are in the current channel). In this case, there are 8 people in the channel called #icechat. On the left is a column called "Nickname" and on the right, one called "Host".
The nicknames do not include the symbols at the start which might include @,% or + (most common). These symbols have special meanings in IRC.
In the "Host" column, the hostmask for the person with that nickname is displayed. A hostmask is in the following format Ident@Host. The ident is nothing you need to worry about but is used by the server. Channel operators can also use it in channel bans. The "Host" part is the most important part. It contains the IP (or host version of the IP) of the person on the channel. This is a number identifying where the connection came from. It is used by the server and can be useful to operators when banning. Channel operators will often ban certain IP's in channels.
You may notice that some nicknames are colored blue in the above example. If you have been on IRC you may notice that some are green and yet others may be orange. Blue ones usually have an @ next to their nick. Orange ones usually contain a % next to theirs, and + symbols are colored green. The colors and symbols show the rank of the person in that channel. The blue ones with @'s are channel operators, or "ops". They can ban people from the channel, kick people out, change the topic, change channel modes etc. Orange ones are half ops – people with not quite as much power as ops. Green ones are said to be "voiced". In IRC some channels can have a special mode called "+m" which means "moderated". This means that people cannot talk unless they are opped, half opped, or are given "voice" (+v). When somebody is given voice in the channel, their nickname will turn green and they will have a + next to their nickname.
Note: On some servers the symbols may be different. But in a vast majority of servers, the above symbols are used.
Note: You can change the colors. They don't necessarily need to be blue, orange, green and black. You can customise them by clicking the "Colors" menu/toolbar item and selecting "Nick List…"