What does the pressure sensor measure? What kind of pressure does it measure? Air pressure? Finger pressure on the touchscreen?
Some devices, like the Motorola Xoom, the Sony Ericsson Xperia Active and the Galaxy Nexus, have an air pressure sensor built into them that measures the barometric air pressure. I have the Barometer HD app installed on my Xoom which seems to give roughly the same reading as my Suunto electronic barometer.

Support for a barometer pressure (and other environmental) sensor was added in Android 2.3 To follow the trend of linking to the related developer resource, I believe this is a TYPE_PRESSURE sensor.

See also this related StackOverflow question Android devices with pressure sensor, and this Gizmodo article for some of the possible uses for the barometer, which includes helping the device  to calculate your altitude in GPS apps.

Android Engineer Dan Morrill made a post to Google+ explaining why the Galaxy Nexus had a barometer internally:


  I've seen a lot of hay made about the barometer in Galaxy Nexus.
  Here's the skinny; it's not really as dramatic or weird as people
  think.
  
  The primary purpose of the barometer is (at least, I've been told) to
  make GPS lockons faster. Locking on to a GPS involves numerically
  solving a 4-dimensional set of linear equations -- 3 dimensions in
  space, and time. (Yes, you get accurate time for free if you lock on
  to GPS.) Because of the way GPS works, this can take a few minutes.
  
  This goes much faster if you already have an estimate of your
  location. This is why "aGPS" (assisted GPS) services are so popular:
  by starting with a rough city-level coordinate fix through something
  like cell-tower network location, you can reduce the amount of math
  you have to do to lock on. This is where the barometer comes in.
  
  The 3 dimensions in space are latitude, longitude... and altitude. The
  barometer gives you a reasonable first-cut estimate for altitude. This
  gives you a bit of a leg up on one of the dimensions -- especially
  combined with "2D" aGPS -- which can help speed up lock-on in general.
  
  Now of course, the barometer can also be used for things like, well,
  determining atmospheric pressure (although I'm not sure it's really
  weather grade.) But the main reason it's in your phone is to help with
  GPS.