I'm not that impressed by the Apple Watch design. I had higher hopes for a band rather than something trying to emulate the style of a traditional watch. I'm sure they'll sell some because it's a fashion accessory and the fitness/health tracking will probably be very useful, but it's not for me.
It might take two years for the technology to come to market, but I think the eventual "winner" is going to be whichever company can make an ultra-light, very thin, flexible OLED-display band that sips power. 3" wide all around, but only 1/4" thick. If it has something like Nokia Glance and senses when you rotate your wrist to display time/notifications, you could easily squeeze a lot of battery life out of such a device.
When that exists at $200 and has the ecosystem to match, I'll buy it. Even Apple is too early for this new wearable segment.
And to answer the OP: what smart wearables will solve is the problem of health/fitness tracking, timekeeping, and notifications, by putting it all into one device on a wrist band or watch. Before smartphones existed, you had separate PDAs, cell phones, GPS units, and mp3 players. There wasn't a true "problem", except for those people who could afford to carry all of those, and found it inconvenient to do so. But once companies started creating smartphones to combine those features, it created a much bigger market, bringing in those people who might not have considered buying all those devices separately. 
It's not likely to be a "must have" category of technology right away, but once the technology and software is there, I can see maybe 50 to 90% of the population getting one. But the technology does need to advance, especially where battery life and customization is concerned. Even for tablets and smartphones people often buy cases and skins just to make them their own, and the need for that is even stronger for an accessory or companion device for your wrist.
Next up: more devices like the Moto Hint, which - like smartwatches - were predicted by sci-fi, like the Ender's Game series (Ender's jewel for communicating with Jane, even subvocally) or "Her". After that: OLED scrolls to replace tablets.