Here is an official looking definition:

Official definition:
"Ping is the name of a standard network utility packaged with popular network operating systems. The utility can be used to determine if a remote device (such as Web or game server) can be reached on the network and, if so, roughly how fast the current connection is. Traditional pings are implemented with the Internet Control Message Protocol (ICMP), although it is possible to achieve a similar effect with UDP or other protocols. Ping utilities send requests to the designated computer at periodic intervals and measure the time it takes for a response packet to arrive. A number of popular "ping tools" that add features to the operating system commands are available on the Net today."

In game, there is multiple usage of ping:

Scoreboard ping – 1 way trip between you and the server (to be confirmed)
Net-graph ping – 2 way or round trip minus any data manipulation delays
Latency – see 2, but not 100% the data manipulation delays are excluded.
Now in plain English:

Noob definition:
Ping is what submarines do, yeah? Same basic philosophy! To give you an idea of how much time (expressed as "ms", meaning milliseconds) is taken between you and the game server communicating with each other, the game server gives you a "ping" number, which it says represents the time taken to send you a packet of information and have it returned. 1000 ms = 1 second.

Your ping in gaming is slightly different, because that is not all that happens – the "packets" that are sent contain information, which each computer has to decipher and then make a response packet. A normal ping program just sends the simplest packet and gets the simplest packet in return.

So if you ping a web server host that is in the same location as the game server, you get a faster ping than what is experienced during a game. But it is a start to understand the importance of this term.

The higher the ping, the worse your gaming experience will be. The further you are away from the server, the more chance you have of not communicating with it in the minimum time needed to stay current with the server.

An analogy is the long distance telephone call – you need to wait for the other person to finish speaking, and for the phone to transmit that, before you can speak, or you will be garbled at the other end. A local call happens quicker.

Ping is also interchangeably described as latency. Latency means the delay caused by the communication time difference between your computer and the server. They mean exactly the same thing (until proven otherwise), although most gamers would use the word ping instead of latency.

Why does my ping change constantly?

Because ping doesn't just depend on distance! It is also impacted by cpu processor speed of the server, the internet servers, the exchanges, other users on your node etc – a whole host of reasons! The ping shown is the average result at the last snapshot, and it constantly re-checked by the server.

Whisper's official definition:
The Maximum amount of Bytes Per Second the Client will request from the server. Rate overrides the servers sv_maxrate setting if rate is less than the servers sv_maxrate setting. b is for bit - B is for Byte - There are 8 bits to a Byte.

Now in plain English:

Noob definition:
Let's say the server wants to send you 100 updates per second, each update containing 200 Bytes. 100 x 200 = 20,000 Bytes of data. Now assume you have a low end adsl connection, meaning downloading at this rate would exceed your connection capabilities. This then means you would lose data from the server. By lowering your rate to 10,000, the server cannot send you 20,000 per second and instead sends you 10,000.

Does this mean you might miss something important? Well, not really. The game allows for this and at your end you will "fill in" the missing information. Things like a barrel twisting through the air - the server will give you position A and C, and your computer will show you the barrel moving between those points, rather than relying on the server for position B. The server will also check to make sure B is correct and fix any client interpolation (eg your computer's guess) errors.

So RATE is really important to avoid clogging up your internet connection and making your game-play smooth. There is no point trying to get 20,000 Bytes from the server per second if this means you cannot UPLOAD your gaming data to the server! How do you know when it is right? Well start with the default rate, and move it up until you see consistent low choke or loss in net_graph display. Minimum rate is usually 5,000, and maximum on 100 tickrate server is 30,000.

Whisper's official definition:
fps is how many frames per second the client is rendering. This is limited by the clients fps_max setting or the refresh rate of the monitors vertical refresh rate if vertical-sync is enabled

Now in plain English:

Noob definition:
Frames per second refers to the number of frames (pictures/snapshots/images) your monitor will show during game play. The higher the number, the smoother your view looks. Your FPS will be limited by your computer's speed (obviously) and your monitor's refresh rate (Hz aka fps).

If your monitor's refresh rate (fps/Hz) is 85Hz, then turning vsync on limits your fps to 85. This means your videocard will only draw 85 frames every second. If you disable vsync, then you are allowing your videocard to draw more than 85 fps. However, this is useless, since your monitor can only show 85 fps (Hz). If you're trying to feed it more than 85 fps, then your videocard will discard some frames and still end up feeding 85Hz to the monitor. So ultimately, above 85 fps or so, your fps (the one you see) is limited by your monitor.

The amount of FPS the human eye can see is discussed here

Back to gaming. You can control how many FPS your monitor shows in 2 ways:

In game, the command is fps_max 100 or 120 etc.
Your monitor will have a Hz setting. You can find this by looking up your monitor properties in control panel / display properties or your monitor manual. It is usually not recommended to ask your monitor to display more fps than the Hz number.
You can force the monitor refresh rate (refresh just refers to how frequently it refreshes the image – and the number is fps) with a number of handy applications, or you can enable "Vertical Sync" in video options in game. Eg: Tweakguides