The airport is actually in Incheon, about an hour from Seoul. While it's a fantastic airport for transiting, I do not think 3 hours is really enough time. Even if everything is on time and your bags are checked through, you need to figure at least 30 minutes to get through immigration and customs into the arrivals hall. And you'd want to be heading back through security I think at least 90 minutes before departure. That leaves you at absolute best 1 hour. I suppose it is do-able if all you do is have a quick cup of coffee in the arrivals hall, but any kind of delay will mess up the meeting.
Note you do not say what nationality you are. If you are American, you do not need a visa to enter Korea, so it's OK. If you are some other nationality make sure you do not need a visa to enter the country if you do this.
My wife is Korean and I am a white American
With the new AREX train, it's no big trip for family members to get to the airport. I would pass immigration to see family members - even for just a few minutes. Immigration at ICN is swift and efficient, and you'd have plenty of time to get your onward flight. You just fill out one short card for immigration (your flight attendant will hand them out before you land). Sounds like you're flying either OZ or KE, so you'll be in the main terminal - this is one of the finest airports in the world.
Information on meeting passengers:
Agree with daawgon. It may not work in case of late incoming but there's a high chance it will.
Thanks to all for helping out someone who is not a very experienced traveler
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