Is there any difference in meaning between "She is not around" and "She is not here"? I heard both, but never quite got the difference.
This is a pretty interesting question. The answer is that there is a difference, but it's kind of subtle.
What they have in common: If someone just isn't present, they are both not here and not around.
Difference: "not here" says that she isn't here, in the room, right at this moment. "not around" is a statement that implies that she will not be around in the future. (Super technical note: That's a simplification. "She's not around" implies that she won't be here in the future relative to the context of the question; see my examples below)
If someone without a mother (either because the mother is dead or moved away) were to be asked "Where's your mother?", a common response would be "She's not around anymore." This automatically gives the idea that she's out of the picture for good.
"We could get your friend's help on this problem. Is he here?" 1) "He's not here." (He's not here -- but we might be able to get him.) 2) "He's not around." (He's not here, and we won't be able to get him for help on this problem)
I think of "she is not around" as being slightly stronger. "She is not here" suggests that she is not in this room right now, but she might still be somewhere nearby, or she might come here soon. So she could still be present in a general way, even if she's not physically at this location - perhaps she is here at work, but right now she's in a meeting. "She is not around" suggests that she is not anywhere close by, in addition to not being right here, right now.
As remarked by both Alan and alexg, "She's not around" suggests greater distance. It also suggests, to my ear, less specific knowledge; if the speaker knew that she were out-of-town, then the speaker would probably say "she's out-of-town." "She's not around," on the other hand, suggests something more like "I haven't seen her for a while, and I know she's gone, but I'm not totally sure where, or for how long."
I also should mention that "she's not around" is, generally speaking, bit more informal.
I think of 'not around' along the same lines as Alan, alexg, and senderle. "not here" is literal, finite--as in "not in this room." On the other hand, "Not around" suggests just that--a broader area that encompasses an area "around" the exact spot (the room) that is being referenced. "Around" connotes something approachable, reachable. In fact, you could even say "She's not here, but she's around."