Whenever a question like this arises, i always go there first:
 
http://auto.howstuffworks.com/question432.htm
Here's another part:
http://auto.howstuffworks.com/car-suspension6.htm 
Some more stuff here:
http://www.edmunds.com/insidel ... olumns/articleId=104166#2
That's just using "anti-roll work" in google btw...
 
Anti-roll cars do what they say, they keep the car from rolling.
You have 3 rotation axis, pitch, roll and yaw. Roll is rotation
around the longitudinal axis (a line from the front to the rear 
intersecting the center of gravity, cog) of the car. It means 
the car 'rolls' around this virtual line. This is usually the case
of a steady-state cornering situation, once the car settles 
into a turn. Anti-roll bars are springs that try to counter this.
They will force the car to remain flat when it tries to roll.
There is usually 2 anti-roll bars, one connecting the 2 front
and another connecting the 2 rear wheels. 
 
As for solid-axles, this is what actually generated the need for
an anti-roll bar. Solid axles usually have one big virtual axis they
rotate around, the driveshaft. As the shaft rotates, it tries to 
rotate the whole rear axle also, this is where various form of 'bars' 
(Panhard,Dion,etc..) were implemented to both keep the axle from
rotating but also to locate the axle as the leaf springs usually
found in such setups, don't constraint the axle laterally (from side 
to side). Considering your axle remains parallel to the ground, the 
torque then tries to rotate the whole chassis around the driveshaft 
instead since it's easier. This rotation is very similar to roll but is 
instead initiated by the driveshaft instead of the chassis. Don't 
mistake 'anti-torque' bars with anti-roll bars. The first usually 
secures the axle to the chassis to prevent the driveshaft from 
rotating the chassis, whereas the anti-roll bars are secured on 
the chassis with each end connected to a wheel by a pivot to
prevent inertia (centipede force) from throwing the whole car 
into the ditch, more on-topic, to prevent the car from leaning 
into a turn.
 
Independant suspensions don't NEED anti-roll bars by definition and 
in fact hinder an independant suspension's work which is usually mentionned
as "anti-roll bars make independant suspensions less independant".
Some very respected 'car guys' have expressed this, but it's still widely 
used to find a good confort/handling compromise. In racing, it's also very
usefull for fine tuning of the handling as they can effectively change the 
front/rear grip ratios giving you more/less understeer/oversteer with
little or negligeable effort. Sometimes, there's even a manual adjustement 
IN the cockpit allowing the driver to tune the bars while racing. If you
forget about the ideal conditions, which racing rarely provide anyways, 
they are also usefull at adapting to changing conditions like adding 
understeer in the rain or conpensate for wear/damage.