When you grab something, you clutch at it. When a party-goer breaks open a piñata, the other guests usually grab wildly at the candy that cascades out of it.
You can grab for the string of a balloon as it floats away, or grab your friend in a hug. Another way to grab is to make an impression: "When I hear a marching band, it grabs my attention." A "grab bag" is a random mixture of things, or a bag of goodies you can reach into and grab from. If something's "up for grabs." it's available: "This last piece of pie is up for grabs!"