Hinged earrings are great--no clip to lose or misplace! But, after they are used for a while, they sometimes become loose and no longer "click" when they are closed. This is easy to fix by slightly bending the post.
The end of the earring's post has a small notch in it. This notch is designed to slide inside another notch which is cut into the opposite side of the earring (see photo), and when it does, you will hear a definite "click". Over time, though, the post can become bent slightly to one side, or upward, which causes the two notches to not line up so the earring will not close. Or the post can become bent down slightly, in which case the notches still line up, but there will not be enough upward pressure to keep the notches together--you will know this because the earring will not "click" when it is closed.
The solution for these conditions is to bend the post ever so slightly back into the correct position. To do this, you will need a pair of small, smooth-tip needle-nose pliers, or just push on the post with your finger. Make sure the inside of the tip of the pliers is not serrated, but smooth, so that you will not scratch the earring post when you grip it with the pliers.
First, make sure the post is lined up with the notch in the opposite side of the earring--you can use your fingers to gently, a little at a time, bend the post back into position so that it will meet the opposite notch when closed. Sometimes, this will be enough to fix the problem, and you will be able to close the earring and hear the "click".
Once you are sure the post is mating with the opposite notch, you can use the pliers, or your finger again, to very, very carefully bend the post very slightly upward. Check to see if the earring clicks, and if not, keep making small adjustments until the earring clicks together properly, but you can still open it without too much trouble. If it clicks together, but is very hard to re-open, you have bent the post a little too far upward, so you will need to make another small adjustment in the opposite direction.
The key is to make your bending adjustments incrementally, in very small amounts, so that you do not break off the post! If you are uncomfortable with making these adjustments yourself, just take the earrings to a local jeweler where they will be happy to adjust them for you, usually for free.