Your easy reference for these paradoxes is here. Two related paradoxes are being referred to.
The paradox where the tortoise can outrun the arrow is the real life 'Achilles and the Tortoise', which you already seem to understand. Achilles (the arrow) can never catch the Tortoise because by the time he reaches the tortoise's position the tortoise has advanced a little - then when he has caught up to that position it has advanced a little more, and so on.
The 'impossible to fall out of a tree' is referred to in the article as "Dichotomy Paradox". In short: in order to fall from the tree to the ground, you must first fall halfway. To fall halfway you must first fall a quarter of the way, and before that an eighth and so on. In fact before travelling ANY DISTANCE AT ALL there is some distance you must travel before doing it. Hence you can never move at all, because there is always some other step (moving a smaller distance) that you must do first.
It's important to note that Zeno (apparently unlike Xeno) didn't believe that movement was impossible, but was pointing it out as a philosophical problem. Essentially he says "Logic tells us this, but this is obviously not true, so where is our logic wrong?". Finding the flaw is quite challenging, and led to some very important mathematical discoveries.