In general, a body organ is a bit of the human body that has a job to do. To get more technical, a body organ is a group of specialised tissues that work together to perform a specific function.
In general usage, the term "body organ" doesn't usually cover the muscles, bones, blood vessels or nerves, although, technically speaking, all components of the human body could be called "body organs".
Our heart is the body organ that is the most prominent in most people's minds - this body organ must be the most widely known. Its function is to pump blood around the body, but a heart is more than that in our thinking. Literature, poetry and general usage all refer to the heart as being bound up with emotions and being the centre. This is logical, seeing as this body organ reacts by speeding up when we're under strong emotions, can be damaged by stress and is in the middle of your chest.
We all know quite a lot about the body organs concerned with reproduction. The organs of reproduction are funny things. After all, does any other body organ have such a wide range of names? Do we get embarrassed about any other body organ? Do we use the name of any other body organ or its function as a swear word ("You bashed my car, you dumb liver! What the digest were you trying to do, pancreas-head?"). Well, OK, I suppose we do use the extreme end of the body organ concerned with excretion as an insult...
We learn about the chief body organs at school: the heart and lungs are the body organs for breathing and pumping blood. The eye is the body organ related to the sense of sight; the ear is the body organ for hearing (and balance), the nose is the body organ for the sense of smell, and so on. And the most important body organ of all is the brain, the control centre for all the other body organs and the body organ that does our thinking.
But we often know less about other organs. If we're lucky, we can remember that the liver is a body organ that secretes the goodies that break down our food and takes out the toxins. And most of us know that kidneys are not just things that get served devilled or with steak but are the body organs that cleanses the blood. The kidney is a particularly interesting body organ, as we actually only need one to get by, but we have been provided with two.
The really obscure body organs are the glands in the endocrine system. This is probably because the functions of these body organs have only been known for the last hundred years and they haven't had time to make their mark in our thinking. The role of an endocrine body organ is to produce hormones. Not just the sex hormones produced in the gonads (ovaries and testicles), either. The pancreas is a body organ that secretes the hormones that regulate our blood sugar (and therefore our energy levels). The pineal gland (located in the brain) is a body organ that regulates our sleep. And the list goes on and on.
To finish with, here's a body organ joke (that's repeatable in mixed company): The biology teacher at the select girls' school had been doing a unit on body organs.
"Now, girls," he said. "Who can tell me which body organ is capable of expanding to twenty times its relaxed state when stimulated? Yes, Mary? Which body organ?"
Mary pursed her lips. "That is a disgusting question and I'm going to tell my father."
"Wrong answer, Mary," said the teacher. "Sally, can you tell us which body organ?"
"Please, sir, it's the pupil of the eye."
"Right, Sally. Now, Mary, three things. Firstly, you should have done that homework I set you last night on the organs of the body. Secondly, you have a dirty mind. And thirdly, one day, you will be very, very disappointed."