The histogram of a digital image is a graphical representation of the number of pixels for each value of intensity.
I find it useful to explain this with a simple analogy: imagine that we create an image with the values \u200b\u200bof the coins of our currency: Any currency is a primary portion of the image (typically associated with what we usually call "pixels") and each coin is obviously associated with a value in cents or in Euro (associated to what we usually call ADU (Analog to Digital Unit "is the unit of luminous intensity of a pixel). Clearly the analogy is not perfect, in fact the most valuable coins are not the brightest (maybe this is why I managed to create a recognizable image ...)
Anyway, here on a composition that should give the idea of a composite image of coins. What is the histogram of this composition? Very simple: just pick up the coins, sort them by value, and rearrange them in a row from lowest to the higher in order to immediately identify which values \u200b\u200bare more in the image.
It is clear that the values \u200b\u200bare more prevalent than those of 1 and 2 cents, while less frequent by 5 cents and 2 euros. Thus the histogram is nothing but a "frequency distribution" ordered by the smallest value to largest value.
But apart from the mathematical definition of what good practice can be a histogram? For normal photography
land histogram can indicate, for instance if the subject is too "overexposed" or otherwise "underexposed" In the first case you would notice a spike in values in the right histogram, namely that corresponding to the brightest pixels in the second case to the contrary, the peak values \u200b\u200bwe would have left the histogram. The histogram clearly also depends on the subject of the picture, especially in the case of astronomical photographs. Let's look at a few examples compared with a normal photograph "Earth." To simplify the discussion, all samples are in black and white and processed 8 bits (256 levels of gray).
The first picture is a classic popular astronomical object: a comet. Even in the case of other entities such as galaxies or nebulae, however, the histogram does not differ much from that mostrato sulla destra. Abbiamo una forte concentrazione di pixel poco luminosi, ovvero sulla sinistra dell'istogramma seguito da un graduale presenza di pixel via via più luminosi. La prima concentrazione altro non rappresenta che il numero di pixel del fondo cielo: non a caso il picco si attesta attorno ai valori 12-13 ADU, proprio quelli indicati come valore di fondo cielo dell'immagine (vedi il valore B nella barra di stato sotto l'immagine). La seconda parte dell'istogramma rappresentato dalla "coda" di valori via via più luminosi identifica la chioma e la coda della cometa con le stelle comprese nel campo di ripresa. Si noti poi il picco intorno al valore 255 ovvero il valore più luminoso per un'immagine a 8 bit: si tratta di tutti quei pixel concentrati in the more luminous (and often saturated) image as the center of the comet's coma and the saturated star in the upper right. 
The second image is a typical extended astronomical object as a planet: Mars. Note now that in this case the sky background image is completely black (B = 0) and that it immediately identifies with the peak vertical histogram at the value 0. The rest of the histogram reflects changes in the gray surface of the planet. The greater the number of pixels around the number 150 and represent the surface of the planet while the lighter brighter focused nell'intorno cap polar and cover a range of values \u200b\u200bfrom 230 to 255.
Finally, as a third example, a typical figure ground: a human face. In a correctly exposed photograph and includes a balanced view of the entire range of gray values \u200b\u200bfrom 0 to 255 with the appearance of the histogram is almost flat. 
