|Gather 'round the campfire|
A curse can be a ritual performed by someone, where the ritual itself causes the damage, for example, Voodoo Dolls or 'The Evil Eye', or it can be an invocation for a deity, demon, dead spirit, or other supernatural entity to do the dirty deed for you. People who make a living out of cursing others, are generally called witches.
Virtually every culture studied by anthropology has some form of curse (and the associated prayer or healing ritual) in that society's myths and rituals.
Due to the connection of a curse as something bad, term 'curse' has come to be associated with society's "bad words". The original curse words might have been true curses "God damn it", but most words that are now called 'curse words' are just 'dirty' words.
Where do curses come from
Anthropology suggests that curses have two or three social aspects which feed into the creation of an idea you can 'curse' someone. Humans seem to biologically prone to ask "Why does something happen", and when even primitive "science like" answers are unavailable, the best answer humans have is that something magical has happened. And of course if the outcome is not good, the magic must have been "not Good". So in a community without science, when things like a sudden heart attack, an outbreak of illness in one family, or the drought that hit one tribe but not another happen, an easy answer is that someone who disliked that person intentionally harmed them, magically.
Another aspect of curses is that the one who 'professionally' invokes curses (by their own design or not), tends to be outcasts of society. Anthropologists note this was a way early societies dealt with people who didn't quite "fit in". The society blamed them for the ills of the society, and they became the local 'witch' of the community.
Finally, there is always the aspect of power. Saying you will curse someone, and having them believe you will curse them, is a powerful tool, even if there is no "magical power". Throughout the history of many so-called primitive societies, as well as early pagan cultures are references to men of power who have 'magicians' who can curse others. In the Bible, there is Pharaoh with his marry band of priests; Gilgamesh finds Shamhat who serves a king; and legendary Chinese Emperors are often associated with magical assistants who curse the enemy.
If there is no magic, why does the myth persist?
Curses actually work. But they don't work because of magic, they work because of self-fulfilling prophecy. The human mind is very susceptible to suggestion , so it is not uncommon for someone who believes they have been cursed, to reinforce that belief with confirmation bias, saying "I tripped today, must be the curse". In more extreme cases, a person can physically make themselves ill because of their belief in the curse.
Curses can even kill people if victims become convinced that they have been cursed to death and cannot survive. The native Australian ceremony of Kurdaitcha or pointing the bone is one example. The effect of the curse is increased by a frightening chant and afterwards the victim is referred to in the past tense to reinforce the belief that he, perhaps she will die, dramatic language is used about how the bone pierces the soul of the victim.  
The healing or removal of the curse works the same way. You believe you've been cured, so you allow yourself to get better, or notice only the good things that happen to you.
Also, because of the oh-so-illusive nature of anything 'supernatural', if a curse doesn't work, you can just say the curse was weak, or that someone invoked a counter curse. Since you cannot prove the curse happened, you also cannot prove it didn't happen, thus leaving it a powerful motivation factor among those who buy into curses.
Curses in modern society
Today, the concept of cursing frequently applies to particular situations that appear to always go bad. For example, every fourth US Presidency was considered cursed since someone noted (correctly or not), that the 4th president kept getting killed or shot at.
Some rather 'famous' curses include:
- The Hope Diamond which causes harm to anyone who touches it.
- The Curse of the Bambino, which insured that the Red Sox would fail to win a World Series
- Voldemort's curse on the Defense Against the Dark Arts teaching position. which prevented any teacher in that position from keeping it for more than one year. None ever did -- it's like it was made up or something.
- Sports Illustrated Cover curse which insures that if you are on the cover, you will either lose the next big event, or get hurt, or just suffer general decline.
- The Bermuda Triangle is said to be cursed, and all ships that enter there will perish.
- ↑ Not to be confused with pagans, 'wiccans', or other modern nice witches, the term 'witch' is used in the common vernacular within anthropology for someone who is an outcast of society and is considered to have access to bad or evil magic.
- ↑ suggestion is the condition that makes hypnotism work, but also the reason advertisers spend so much on tv ads; suggestion is culpable in the mental condition of hypochondria, and is one of the reasons we elect who we do for president.
- ↑ http://everything2.com/title/Kurdaitcha
- ↑ http://www.museumstuff.com/learn/topics/Kurdaitcha
- ↑ See the Wikipedia article on Hope diamond.