When you rub the balloon on your head it gains a charge. By removing either the positive or the negative charges from your head, the balloon is left with either an excess of the other charge (positive or negative). Lets say the balloon is left with an excess of positive charges.
Now when another object like the wall is near, the charge on the balloon "induces" the charges in the wall. The negative charges in the wall are drawn toward the positive charges in the balloon. This pulls the two together.
If the balloons stick to your skin, it is the same principle. The balloon has more of a positive charge and that gets drawn towards the negative charge on your skin.
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