(1) Everyone has the right to freedom of movement and residence within the borders of each state.
(2) Everyone has the right to leave any country, including his own, and to return to his country.
(1) Everyone has the right to seek and to enjoy in other countries asylum from persecution.
(2) This right may not be invoked in the case of prosecutions genuinely arising from non-political crimes or from acts contrary to the purposes and principles of the United Nations.
(1) Everyone has the right to a nationality.
(2) No one shall be arbitrarily deprived of his nationality nor denied the right to change his nationality.
But what does this mean for me?
Now, of course these rights are subject to criminal prosecution; if you've been convicted of a felony, then your right to move around within the country is going to be somewhat hampered by the 7x10 cell that you call home; if that felony happens to be child molestation, your freedom of residence is going to be somewhat hampered by any elementary schools nearby. But as long as you're a decent, law-abiding person, you get to go pretty much where you need/want to go. It's kind of like a really understanding mother; if you behave yourself, she's likely to trust you and let you hang out with your friends and give you a late curfew.
But let's say your mother isn't so understanding, and despite your good behavior, she's going to ground you for a multitude of offenses. In that case, you also have the right to go next door to seek asylum from Mr. and Mrs. Canada, the really nice old couple that lives there. However, if it turns out you're grounded for an offense punishable by reasonable grounding, those kind old folks are likely to march you right back to your mom. Sometimes it happens that way.
And when you get there, your mom'll probably be plenty pissed off, but one thing she won't do (as an understanding mom) is disown you. You're her kid, and even when you misbehave, she loves you. Just like the US government loves you and won't call you unamerican just because you do something that pisses them off.
Wait, no, hold on...
Just answer the question already.
It means that home is home, and you're not going to get kicked out of home. And if home isn't treating you right, you've always got a place to go.
Part I: The Preamble; Part II: Articles 1 and 2; Part III: Articles 3 and 4; Part IV: Articles 5 and 6; Part V: Articles 7 and 8; Part VI: Articles 9 and 10; Part VII: Articles 11 and 12