The Meter Toolbar is used for monitoring the input and output audio levels. Typically it is used to make sure that the average volume is as loud as possible (for maximum fidelity) without clipping. The output (playback) meter is the green one, on the left pictured above, and the input (recording) meter is in red, on the right.
If you float the Meter Toolbar, either by dragging it out of the toolbar or by selecting "Float Meter Toolbar" from the View menu, you can resize it and even orient it vertically.
Normally the meters are only active when you are playing or recording audio. However, you can also monitor input when you're not recording - to do this, either select "Monitor Input" from the input meter's pop-up menu, or else just click on the input meter. If you have a microphone or other input source attached, you will be able to watch the level of the audio before you start recording.
Each meter shows several characteristics of the audio level at once. For stereo, the top bar shows the left channel, and the bottom bar shows the right channel. The brightest part of the bar shows the average audio level. The darker part of the bar shows the peak audio level. The peak-hold line to the right of this shows the maximum audio level achieved in the last 3 seconds. Finally, the clipping indicators on the far right of each meter will light up if clipping is detected (meaning that the audio was too loud and will sound distorted). If clipping is detected when you are recording, you should stop, lower the volume of your input source, and start recording again from the start.
If the level of the input (recording) source is too high, you can try to lower the input level using the Mixer Toolbar, but if this doesn't work, you should try to lower the volume of the external input source (e.g., your microphone, cassette player, or record player).
It is possible, especially if you have an older, slower computer, that the Meter Toolbar may interfere with Audacity's ability to record or play audio with the highest quality, because your computer is so busy redrawing the meters that it doesn't have time to process enough audio. In this is the case for you, you can disable the Meter Toolbar in the Interface tab of the Preferences dialog.