Profanity means bad/swear words, and/or using vulgar/offensive language. The adjective is profane. Profanities can also be called curse ("cuss") words, dirty words, bad words, foul language, obscenity, obscene language, or expletives. It can be called swearing, although this also has a normal meaning of making a "solemn promise". A profanity usually refers to religion, sex, or bodily functions. These are things that people feel very strongly about. In some languages, such as French, there is more profanity about religion than most other topics. This is the original meaning, from a Latin word meaning "before the temple".  

Religious profanity is called blasphemy. The verb is to blaspheme and the adjective is 'blasphemous'. Saying “God!” or “Jesus Christ!” as an expression of surprise or annoyance is considered by many to be blasphemy, mostly because one of the Ten Commandments says not to use God's name "in vain" (without substance or without relevance). Swearing oaths can also be considered wrong by some who follow Jesus' teaching against swearing oaths in the Gospels (such as Matthew 5:34).

A profanity can be a word or gesture or some other form of behavior.

Different words can be profane to different people, and what words are thought of as profanity in English can change over time.

Whether a word is a profanity will always depend on the way people think. Some people will be offended by something, while others will not be. Words which should not be used are taboo words. Using such words is thought by some people to be a sin. For example, some Christians and some Muslims believe that swearing is a sin.

Opinions on profanity 
Some people call profanity "crude," but some say that it is no cruder to say "damn" or "crap" than it is to use "hate" (a word that is about a very strong emotion, but not a swear word). People who use profanity do not always mean to make anybody feel bad, and tolerance for different forms of profanity can vary widely, from person to person. Most often, using profanity is a verbal outlet for strong feelings (usually unpleasant ones), that might otherwise cause a physical reaction. At other times, some people may use profanity as humor.

Coprolalia 
Coprolalia is a mental condition that makes people use profanity constantly. It is different from Tourette syndrome. Tourette syndrome is actually a group of symptoms that only includes coprolalia 15% of the time. The condition can be made worse by stress.

Examples of profanity 
Several of these words come from Anglo-Saxon or old Norse names for body parts, and bodily functions. They came to be thought of as profanity mostly after the Normans brought French and Latin words for them to England.  

Ass (or Arse)

Means the buttocks.    
 
Asshole (or Arsehole)

Means the anus. Also used as an insult for a mean and unpleasant person.

Bastard 

A term for a child who was born to unmarried parents. Also used as an insult for an unpleasant person.    

Bitch 

A female dog. Also used as an insult for a disliked woman.

Cock (or Dick)

These terms refer to the penis, and/or as an insult for a unpleasant person or a fool.

Cunt (or Pussy)

A vagina. Also used as an insult for a disliked person.

Fuck 

A verb, meaning to have sex.

Piss

Urine; also a verb, meaning to urinate. 

Shit (or Shite) 

Feces; also a verb, meaning to defecate.

Profane gestures 
These are mostly performed while facing another person and can be meant toward them, or about them. These gestures are considered as strong as profane words in most cases.

 Biting one's thumb
 Performed by placing the tip of a thumb under the front teeth, then pulling the thumb slightly forward, with the fingers closed. Mocks the "thumbs up" gesture. Can be taken to mean "bite me", though it predates the common use of this phrase.

Grabbing one's own crotch
Also an invitation to "bite me", or to perform oral sex in a  way.

 Pretending to give fellatio
 One pokes out a cheek with the tongue while rocking a closed hand toward the mouth, at the same time. Indicates something or someone is a waste of time.

Pretending to masturbate
Indicates something or someone is a waste of time, or performs poorly.

Showing one's middle finger ("flipping the bird")
Understood generally to mean "fuck you" or "fuck off".

Showing a reversed "V" sign
Understood generally to mean "fuck you" or "fuck off".

Thumbing (or "fluting") one's nose
Performed by placing the tip of a thumb against the tip of the nose, then wiggling the fingers. Expresses , or thinking that someone is foolish.

"Up yours"
One turns a forearm horizontally while swinging the other fist and forearm around it. Suggests something being shoved into a person's . If the middle finger is shown, it is a stronger form of "fuck you", or a suggestion of anal sex.

References

 
Human communication
Obscenity