Glad you asked. :)
A third culture kid(TCK) is someone who has spent at least part of their childhood in countries and cultures other than their own. Below is a better explanation than I could fumble out:
"Children are TCKs for many reasons. Some have parents with careers in international business, the diplomatic corps, the military, or religious missions [me!]. Others have parents who studied abroad. Still other families live for a period of time outside their home culture because of civil unrest and war.
TCKs are raised in a neither/nor world. It is neither fully the world of their parents' culture (or cultures) nor fully the world of the other culture (or cultures) in which they were raised....[As a result of this,] TCKs develop their own life patterns different from those who are basically born and bred in one place. Most TCKs learn to live comfortably in this world, whether they stop to define it or not." -Third Culture Kids by David C. Pollock and Ruth E Van Reken
These kids have created a third culture - one that is neither their parents' or the host country's - thus comes the name: Third Culture Kid.
There are a lot of us TCKs floating around. You might be surprised by just how many there are, though a lot of us don't even know we are TCKs. Unfortunately, though it is becoming more widespread, this term is not a widely used as it should be.
Many TCKs struggle through their lives never really fitting in anywhere, feeling like the outsider, and thinking it's somehow their own fault. It's a horrible place to be; as I know from experience. My high school years were very lonely. I couldn't relate to my American peers, but I in no way looked or sounded like I was from the African countries I spent my childhood in - though they had profoundly impacted my worldview. It wasn't until my mom came across Third Culture Kids, the book quoted above, that I realized how much of an effect culture had on my life experiences; and finally understood why it was such a struggle to connect. The kids here had no idea what my life had been like growing up. And though I had some exposure to American culture through my dad and our brief intervals States-side, I had not been in the US long enough to have a knowledge bank of the cultural expectations and trends. It helped to know that. My social life was not automatically "fixed", but it became easier over time - especially as I matured and entered college - to find points of connection and ways to be a part of society that didn't stifle the value of my past experiences or discredit the culture I live in now. (The field of education, especially, has been a good venue!) Which, I guess, is the goal everyone strives for in some way or another - even within their own culture.
There's more I could say, but that's all for now.