The card you are asking about is a Guest Assistance Card.
GAC is our abbreviation for Guest Assistance Card. GACs are not meant to (and usually won't) shorten or eliminate the time spent waiting in line.
In general, it's a tool for CMs to know what sorts of assistance are needed by people with invisible disabilities. The GAC is based on the needs of the person, not their diagnosis (since people with the same diagnosis can have vety differnt needs).
As was already mentioned, that might be things like needing extra time to board rides or needing a quieter space to wait. The GAC is individualized to the needs of person it is issued to; so someone who needs to wait out of the sun will have a GAC with something like "allow to wait in a shaded area when the queue is in the sun for extended periods of time." The GACs don't actually have a long message like that; they have a quick to interprey icon (picture), so that the CMs don't have to read it carefully.
GACs are requested at Guest Services in any park.
I don't know what your disability is, but if it's concerns with standing or walking, you would probably be better off considering a wheelchair or
ecv. That is the usual response that WDW has to what they call "Stamina or Endurance Concerns" and is probably what you will be told if you ask about a GAC with those types of needs. That makes sense since walking in lines is just a tiny portion of the walking done at WDW during a day.
Most people who use a wheelchair or ecv don't need a GAC because the CM can tell what is needed (ie. an accessible route into the ride).
If you decide on a wheelchair or ecv, there is a FAQs thread at the top of the disABILITIES Board with a lot of info about wheelchairs.