Canon's flashes are named for the "guide number" of the flash. E.g. the 430EX II has a guide number of 43 (meters), the 580EX II has a guide number of 58, etc.
The guide number is the distance at which the flash can deliver enough light for an adequate exposure using ISO 100 and f/1.0 It can be expressed in either meters or feet but Canon uses meters.
While every camera can do ISO 100, virtually no camera/lens can do f/1.0 (Canon did make a 50mm f/1.0 lens but they haven't made that lens in well over 10 years.)
The reason f/1.0 is used (even though you can't take an f/1.0 exposure) is that it makes the math VERY easy. Just divide the guide number of the flash by the ACTUAL f-stop you're using and you'll arrive at the distance that the flash can handle.
For example, if you're shooting at f/5.6, divide 43 meters (141 feet) by 5.6 and you get a distance of about 25 feet. The 580 (guide number of 58) works out to about 190', but divide that by f/5.6 and you get about 34' working distance.
Keep in mind that this is all at ISO 100. Each time you double the ISO you can increase that distance by 1.4 (the square root of 2).
While these distances might seem large, something else to keep in mind is that most diffusers will eat about 1 stop worth of light (fire through a frosted glass, plastic, or shoot-through fabric and usually about half the light penetrates the diffuser (this is a guideline... TEST your diffusers so that you know how much light they eat.) If you "bounce" the flash, then you've got to measure the distance up to your ceiling or wall, then back to your subject AND account for the fact that the bounce surface wont actually reflect 100% of the light. Suddenly a flash that shoots 25' (at f/5.6) can be reduced to less than half that value. You can crank up the ISO to get your distance back, but higher ISO increases the noise.
The 430EX II is a reliable workhorse flash and it's great for most personal shooting situations. I can work as a "slave" flash but as was mentioned above, it cannot be a "master". The 580EX II does everything the 430 can do, but can also work as a master (or slave), has a built-in bounce/catch-light card, supports multi-strobic shooting (you can program a series of flashes at a specific interval within just one frame... it catches a moving subject in multiple positions) and it's weather sealed. It also has an external sync cord connector and can accept an external battery back for extended shooting. It's a bit more of a pro level flash.
The new 600RT does everything the 580 can do but also supports radio triggering (this requires that you either have one of the newer Canon bodies with radio triggering or you buy the radio trigger controller.)
I have all three of these flashes. Depending on what I needed to shoot, I'd often just grab the 430 because it's smaller & lighter if I didn't need the power or features of the larger flashes. However, if I only had 1 flash at a wedding, then I'd minimally want a 580. The 430 might be a nice economical second light, but you'll find it's not quite enough for some large rooms. ALSO... guide numbers assume the reflector on the flash is concentrating the beam. At a wide angle the beam disperses more rapidly (think "group shots").