TYPICAL ERROR If your certain that you're sister will not mind, then I will borrow her racquet.
CORRECTION If you're certain that your sister will not mind, then I will borrow her racquet.
EXPLANATION You're is a shortened form of you are. When words are shortened this way, we say that they are contracted (which means drawn together because the Latin tract means to draw, as in tractor or retract). The apostrophe in you're indicates that the a has been taken out. We should actually pronounce the you in you're as you (so that you're rhymes with fewer). So, you're rhymes with fewer; your rhymes with floor.
Your is a possessive pronoun, and there is the same difference between your and you're as between their and they're.
Insert you're or your in these sentences as appropriate.