To answer this question, one has to identify the characters who make the accusations and then determine their possible motive/s.
Abigail Williams, a teenager previously in the employ of John and Elizabeth Proctor, had been dismissed from her post by Elizabeth. John was involved in an adulterous affair with Abigail and Elizabeth discovered his betrayal and thus dismissed her. Abigail targets Elizabeth out of vengeance. She also sees the trials as an opportunity to reunite with John once Elizabeth is out of the way.
Added to this, Abigail played a major role in encouraging the girls to summon spirits in the woods under Tituba's guidance. When her uncle, Reverend Parris, discovers them 'dancing in the woods,' she finds that levelling accusations at others the best way to absolve herself from blame. She is an innocent victim of others' evil.
The Reverend Parris has always been reprimanded by John Proctor for his materialism. Parris has been publicly admonished by John, which has brought the paranoid Reverend much anxiety. He believes that John's constant criticism has led to the Salem parishioners' disdain for him. As a result, Parris repeatedly meddles in the hearings, mentioning details about John's supposed infringements, such as that he is not a regular churchgoer, and so on. The witch-trials are an ideal opportunity for the Reverend to get back at whom he sees is his greatest enemy. Also, with John out of the way, his position is secure.
The Putnams have been in regular dispute with a number of villagers over land. They want to take revenge on those who they believe have denied them their rightful claim, such as Giles Corey, John Proctor and the Nurses. Mrs. Putnam also resents Rebecca Nurse for having given birth to many healthy children whilst she had lost so many of her babies.
Reverend Parris seeks to enrich himself and has requested the title deeds to the rectory. He has consistently sought gold candlesticks for his pulpit and is deeply dissatisfied about the remittance he receives. John Proctor has constantly denounced him for his materialism. With John out of the way, he can continue enriching himself. The same applies to Rebecca Nurse - once she is gone, the Reverend is free of her criticism as well. Since both of these characters are strong leaders in the village, their execution would free him from the risk of losing his position.
Mr. Putnam seeks to gain others' land through foul means. He encourages his daughter, Ruth, to accuse those whose land he can acquire of witchcraft. Once an accused is found guilty, the state takes possession of his property, which is then sold at auction. Mr. Putnam has the financial resources to buy such land cheaply. It is for this reason that Ruth, for example, accuses Mr. Jacobs. Mr. Putnam eventually becomes the one who lodges the greatest number of charges against innocent villagers.
Those are the two most pertinent reasons why false accusations of witchcraft were lodged against the innocent.