A false accusation of child sexual abuse is a defamatory allegation against another person of a sex crime against a child that did not occur. On p23 of Tara Ney's True and false allegations of child sexual abuse: assessment and case management, false allegations of child sexual abuse are defined as, quote: 
An allegation that is wholly untrue; that is, one in which none of the alleged events occurred.
An allegation in which an innocent person has been accused but the allegation is otherwise valid. This is a case of "perpetrator substitution" in which an abused child discloses his/her abuse but accuses someone other than the actual perpetrator.
An allegation that contains a mixture of true and false features; that is, the child describes some events that actually occurred and adds other that did not.
Click here to view a preview of the aforementioned text from Tara Ney's True and false allegations of child sexual abuse: assessment and case management on Google Books.
Who perpetrates false accusations of child sexual abuse?
False accusations of child abuse can be concocted by spouses, distant relatives, sexual partners, ex-partners, friends and acquaintances, though women are more likely to be believed when they accuse their husband during a custodial dispute over their children. 
Only a minority of allegations are conducted by children. 
What causes an adult to falsely accuse someone of sexually abusing a child?
There are usually four reasons adults falsely accuse other people of sexually abusing a child:
Malevolent desire to hurt the accused
Fear of losing one's children
Misplaced concern about other people's children.
Custodial Disputes and Divorce Hearings
Allegations filed during custodial disputes and divorce hearings usually arise from the desire to gain custody and/or to hurt their significant other.  A parent might try to add credibility to their false accusation by brainwashing their child into agreeing to testify against the accused.  Mental illness on behalf of the accuser can lead them to believe their significant other committed the alleged crime.
In general, the timing of the allegation is crucial in determining its validity. For example, a person who says their significant other abused their child for years would look suspicious if the first time they stated this was during a recent divorce hearing. Suspicion would be cast upon the person in the aforementioned for two reasons: a) they stand to benefit from it and b) they did not report the alleged abuse earlier.
Allegations filed outside of custodial disputes and divorce hearings by distant relatives, neighbours and acquaintances
An accusation started by a distant relative or acquaintance can stem from the malevolent desire to hurt the accused, though it's probably more likely to stem from ignorance, stupidity and hysteria. People might assume a stranger or a neighbour who behaves abnormally must be guilty of abusing children. Stereotyping can play a key role in these sort of cases. It's not uncommon for people to be suspicious of men who are regularly around children or caught alone with a child. This has led to men feeling afraid to help unsupervised children in danger.  Feminist propaganda about sexual abuse and the mythical patriarchy fuel society's stereotypical attitude towards men who are around children.
Effects on the accused
Persons wrongly accused of sexually abusing a child are often viewed with suspicion by friends, family, neighbours and acquaintances, even when their name is cleared. Some people are outcast from their social circle and required to rebuild their lives elsewhere. Depending upon the age of the alleged victim of child abuse, it can cause long-standing tension between them and the accused. For example, a child might wonder whether the accusation is true if it was made when they were too young to remember.
Around 10 per cent of child sexual abuse allegations are believed to be untrue, though the incidence rate varies from study to study.  For example, several studies from the 1987 to 1995 period found anywhere from 6% to 35% of reported child sexual abuse allegations were false. The variance in the data of the studies from 1987 and 1995 is believed to be due to methodology, with the ones only counting intentional deceit on behalf of the accusers tending to fall in the lower section of the range, while the converse held true for the ones that counted intentional deceit along with mistaken assumptions about other people.
According to Melvin Guyer, Professor of Psychology at University of Michigan Guyer said, "in highly contested custody cases where the allegation is made, a number of researchers have found the allegations to be false or unsubstantiated in anywhere from 60 to 80% of those cases". 
Sexual Allegations in Divorce Syndrome
Due to the commonality of such claims during divorce hearings, an acronym known as Sexual Allegations in Divorce (S.A.I.D.) Syndrome is used to describe instances in which one spouse makes a false accusation of sexual abuse against the other. 
The exponential increase of S.A.I.D. could be derived from the influence of chivalry and feminist-indoctrination within the legal system. Under feminist ideology, a woman's accusation is considered irrefutable and must be used to decide the case in her favour -- they argue that failure to abide by this technique is an example of misogyny and oppression. Political correctness may play a role as well, since it depicts the act of not treating a woman more favourably than a man as a form of impolite resentment towards women. Another reason for the increase of S.A.I.D. could be derived from the fact mothers are more likely than fathers to be believed when bringing false accusations of child abuse into court proceedings, as Aaron Larson pointed out.