In "The Crucible", what role does Parris play during the testimony? Why does he lie about the dancing in the woods?

In act three, we really see how Parris works in the courts.  He insinuates himself into everything that the court does--he offers opinions, he offers background information about everyone that comes forward, he asks the people questions, and even seems to act like an unofficial judge. He has become quite the busy-body, holding himself above others, feeling very spiffy in his special role as a little helper to the courts and the judges.  Unfortunately, he doesn't really present a fair and balanced perspective; his entire purpose in being there is to cover up any potential reputation-ruining blame on himself, to protect his own welfare, and, it seems, to vent his frustrations against anyone that has ever slighted him.

When Giles Corey comes to the courts, and the judges ask who he is, Parris doesn't just introduce Giles, he throws in that Giles is the most "contentious" person that they will ever come across.  Right away, he is setting the judges against Giles--not coincindentally, Giles is one of the men that Parris has argued with in the past.  When John Proctor comes, Parris immediately asserts, "They're trying to overthrow the courts!" before John has barely even had time to speak.  This automatically sets the courts against John, and sure enough, the are constantly suspicious of his intentions there.  Parris and John have argued vehemently in the past, and, John holds potential evidence to prove Abby, Parris's niece, a liar, and to prove they were doing evil deeds in the forest.  If Mary's testimony in this regards gets out, Parris's reputation will be ruined--witchcraft in his own house, from his own niece!  He'll be finished.

So, when the dancing is brought up by John, Parris immediately and defensively jumps in, saying, "since I came to Salem this man is blackening my name," and then tries to shimmy out of having any knowledge about the dancing.  He doesn't want that being attached to his "good" reputation in the town.

Parris goads, questions, pries, insinuates, taints and noses about in all of the questionings, inserting his own viewpoints, and nudging things in a direction favorable only to himself and his pride.  Even Danforth is a bit irritated with him; at one point he bursts forth, "Mr. Parris I bid you be quiet!"  Parris fancies himself an unofficial judge, and uses that position to his own advantage.  I hope that those thoughts helped; good luck!