You can find the story of the test of the bow in Chapter 21. It is the point at which Odysseus really comes out and declares who he is in front of the suitors.
The test was that Penelope says that she will marry whichever suitor can string the bow and then shoot an arrow through 12 axe handles. None of the suitors can even string the bow so none of them even gets a shot at the axe handles.
The reason that this is so hard is that the bow is very stiff. A stiffer bow is more powerful, but it is much harder to use -- you have to be way stronger. So this is a way of showing that Odysseus is much stronger than any of the suitors.
The test of the bow is Penelope's test for the suitors. She claims that she will marry the man who can complete this test because he will be much like Odysseus.
The man who completes this will be able to string Odysseus' bow. Then, he will shoot an arrow through twelve ax head handles. This is a very difficult task to complete because no one has strung the bow since Odysseus did it, and it takes great strength. Secondly, this is difficult because it will take great precision and concentration to get the arrow through that narrow set of goals. It's not just one target.