At the beginning of Act 5, the scene opens with two gravediggers who are preparing Ophelia's grave. Remember that we just learned that Ophelia died a rather strange death by drowning at the end of Act 4. The question they are debating is whether Ophelia intended to kill herself, or if it was an accident. Was she sane enough to know to what was happening? Why didn't she at least try to save herself? This question is an important one during this time period because suicides where not allowed to buried in blessed Christian burial because suicide is the ultimate mortal sin against God and there is no chance for forgiveness or redemption.
The play indicates these characters as "clowns" which was an indication of their purpose in the play: to provide some comic relief. While the subject of their discussion is heavy and dark, their handling of it is funny, dark humor. For example, one of the grave diggers tries to sound very smart and official. He explains that "an act hath three branches -- it is to act, to do, and to perform; argal, she drowned herself wittingly." This is funny because the three branches he mentions are actually all synonyms for each other and then instead of using the proper word, "ergo" meaning "it follows" he uses the a mis-word "argal." After that he jokingly acts out the scene of her drowning, which would probably have elements of physical comedy when seen in a live performance.
Ultimately, they are implying that she did, in fact, kill herself but because of her family connections to the King, she will receive a proper burial. He specifically states, "If this had not been a gentlewoman, she should have been buried out o' Christian burial."