I work in outreach, so I emphatically believe in finding clear ways to inform others about things in general, and so have worked through different ways to effectively describe it. I come from a family full of diabetics and have found that be a useful comparison as it is a similar condition in many respects but far better known than Narcolepsy.
Both narcolepsy and diabetes require lifestyle changes
-diabetes: you must monitor blood sugar levels, watch what you eat, schedule meals carefully (even when people want to eat at other times, or food that is not good for you, etc.)
-narcolepsy: you must monitor your wakefulness, schedule sleep carefully (even when people want to hang out into the evening, or when there is something funner to do than have an afternoon nap that you require), and to a certain extent even watching what you eat to prevent sugar/caffeine crashes
Neither narcolepsy nor diabetes are terminal, but mis-managed they are potentially life-threatening
-diabetes: carelessness about what you are eating can cause severe complications
-narcolepsy: falling asleep while driving, operating machinery, etc., could end in severe injury or fatality
Both diabetes and narcolepsy require making the "right" small decisions many times throughout the day
-diabetes: saying "no" to a favourite food that is high in sugar, forcing yourself to go out and exercise even when you don't feel like it, communicating with others if there is a potential for complication (e.g. if there is a chance that you will have a severe low, having to explain to people what you need them to do), keeping emergency supplies on hand, staying in regular communication with a doctor who specializes in your condition and taking required medications on schedule
-narcolepsy: saying "no" to forcing yourself to stay awake at certain times, and at others having to find ways to ensure that you can stay awake, communicating with others and ensuring that you have a great support network of friends/family who are going to assist you in maintaining a regular schedule, won't judge when you are "out of it" because you're tired, and who know how to respond in case of severe narcolepsy, staying in regular communication with a doctor who specializes in your condition and taking required medications on schedule
Even managed with diligence, both conditions may or may not evolve and/or worsen over time
Both conditions may present due to genetics, environmental factors, or just plain happenstance
(I mention this because there is a co-relation to sustained food choices and diabetes, particularly in the US right now, but coming from a mostly healthy family where it is sort of more "un-luck of the draw" for who gets diabetes I feel that it is important to point out, especially because my parents in particular really struggle with the why and how of narcolepsy)
I have also found that quantifiable examples help... I learned this when I said to my sleep doctor at my intake interview "I always fall asleep while driving". He later summarized "So, that's maybe once a month or so you are tired while driving?", and I had to clarify "No. Every-single-time I get into a car and drive I fall asleep - whether driving around the corner, or on a longer trip. Every time. And when I say "fall asleep", I mean that I am jolted awake by my hands hitting my legs after they have fallen off the wheel". No pun intended, but that was an eye opener for him...
Thing is, sleep and sleepiness are familiar to everyone in the whole wide world, and perception is relative so it is difficult to really convey what exactly is different about narcoleptics and anyone who is exhausted because of work, partying the night before, raising kids, what-have-you. Frankly, I find it understandable that people have trouble getting it, and that is where this "quantifiable examples" idea comes from...
I mangle a quote from somewhere online and instead of saying that I get extremely/very/super/extraordinarily sleepy, I say something like "Even after a good night's sleep, it is possible that suddenly I will feel tired. Doctors have estimated that when a narcoleptic says 'tired' they are feeling about the same as someone who has been sleep deprived for approximately 4 days."
Another one that I think is key: "Narcoleptics usually get the same number of deep sleep hours as a typical person, but they are spread out more throughout the day because the same patterns that are disrupted during the day causing me to fall into sleep prevent me from falling into deep sleep at night".