A barometer measures atmospheric pressure, which can help give you a rough idea of how the weather will be changing in the next 24 hours.
It's not so much the actual number reading as the trend the readings are taking. A steadily falling barometer usually signals a storm is approaching, while a rising barometer normally means sunnier skies ahead. Although very low readings (under 29.50 inches) can suggest a strong storm approaching.
If sea-level pressures are under 29.20, look out. That could mean very strong winds are on the way.
Barometer readings usually range from about 29.70 to 30.20 or so, with 29.92 being the average reading.
Check this link to get the current barometer setting for your city. It's listed under "PRES". Ignore the letter, that's the current trend.
And learn more about Sea Level Pressure from the Jan. 1, 2003 Ask Steve column.