Yes.  To be more precise.  Digital ISO correspond to ISO film speed
so that a digital camera set to a specific ISO setting should be set
to receive the same exposure (i.e. aperture and shutter speed) as a
film camera loaded with a film having the same ISO.  (YMMV - but my
experience is that "sunny 16" works pretty much the same with digital
as it does with film).

Noisy.  Increasing the ISO speed of a digicam increases noise.
It is a bit like film grain, but IMHO - it looks worse.  Take
a look at the tests at dpreview.com to see how noise at high
ISO values look like - they usually test dSLRS up to their
highest possible ISO setting.

The ISO setting goes to the sensitivity of the sensor.  The sensor itself is a
constant gain sensor, but in between it and the analog-> digital converters is
a gain section.

1) It sets the amplification of the signal received on the sensors prior to
conversion into digital

2) Its setting is what the metering systems uses along with aperture and shutter
speed to determine if the exposure is correct.  In "auto" modes, the camera will
evaluate the light and choose the optimal ISO/shutter speed/aperture.  In semi
auto modes such as aperture priority, it will set the shutter speed based on
your choice of ISO and aperture.

Digital sensors have constant "grain" regardless of the ISO.  But the noise in
each pixel may be higher as the ISO goes up resulting in 'speckles' due to the
difference in noise in adjacent sensors.

Cheers,
Alan