Cables are lossy at high frequencies.
The TV TMDS receiver chip has limited sensitivity.
The signal is launched at a high amplitude, and shrinks
as it goes down the cable. If the received amplitude is
not sufficient to trigger the TMDS receiver properly,
you see "digital noise" as colored speckles on the LCD screen.
At some point, the circuitry after the receiver declares
there is no valid signal, and the screen goes blank.
"Boosting" means signal regeneration. Signal regeneration
can be of two types. Naive regeneration is simply an amplifier.
The problem with that is, it can add jitter to the signal.
Time domain jitter, degrades the eye diagram when you try to
receive the data at the receiver.
Full digital regeneration, would intercept all the bits, recover
the clock, then clock out the data using a built-in PLL. The
idea would be, the PLL would be a low-jitter way, of launching
the data on the outgoing side of the booster.
So that's the basic concept.
Now, the HDMI standard, may not have a "you must never use more
than X meters of cable" thing to it. If the cables are cheaply
made, they might only be good to 3 meters length. A better
quality cable might double or triple the length (depending
on who you believe). Then, bodging together boosters might
further increase the potential range (until things like
HDCP break due to protocol problems caused by all the
garbage used to carry the signal). It's very much the
kind of business the folks at Monster Cables would
want to sink their teeth into
(Plenty of opportunities
to extol the virtues of gold plated this and that.)
In other words, if you keep the computer close to the TV,
it doesn't cost too much to make the connection. If you
want to run a TV on the other side of the house, it could
be more expensive, and involve testing and returning stuff
to the store.
You can go further than copper cabling (regular HDMI cables),
by using fiber optic cabling and active optical transceivers.
This is the first example of using fiber optics to do the job
that I could find. You can see the prices here, are pretty high.
http://www.dvigear.com/hdfiopca.html
Have fun,
Paul