In Proctor's final speech, he comes to accept himself. This has been his struggle throughout the play. In addition to striving against the corruption of the court, he has had to fight against the sense that he has been irrevocably tainted by his affair with Abigail.
In his last speech, Proctor says that he now sees "some shred of goodness" in himself. This is all he needs to feel capable of honorable sacrifice and he chooses to go to the gallows instead of signing a false confession.
Up to this point, he had wondered if he was morally qualified to make a meaningful sacrifice, thinking that he was too weak and compromised to do so. Hale and Elizabeth convince him otherwise and in this final speech, Proctor acknowledges that he has not been defeated - morally or spiritually - by the witch trials. Against the mob, he has struggled but maintained (or even regained) some integrity and honor.
This speech is important because it gives expression to the nature of the conflict involved in the trials. Though on one level the trials were about conformity and hysteria, on another level they were about individual responsibility.
...wrong-headed actions such as the witch trials - are often motivated by a lack of personal responsibility rather than based upon deliberate cruelty or malice.
John Proctor speaks out against the trials and also takes responsibility for his mistakes with Abigail. He refuses to falsely condemn others with a signed confession. His last speech solidifies the meaning of this choice - the individual's relation to his soul remains the responsibility of the individual, no matter what the group says or does.
John Proctor's last speech in Act III is important because it points out that he knows what the court in Salem is doing is wrong and that they will all be punished for allowing innocent people to die. It is also showing that he not only thinks the members of the court are to blame but that he is as well because he did not come forward when it all started and tell the court that Abigail was lying because he didn't want people to know he was a "lecher".