A Petri dish is a common piece of microbiology laboratory equipment which may be made of glass or transparent plastic. It is a round, shallow dish with a flat bottom and vertical sides. It comes with a lid which is slightly larger and thus fits over the sides of the dish. Petri dishes are generally used to hold agar or gelatin growth media for the purpose of culturing cells and microbes such as yeasts and bacteria.
The invention of the dish is most commonly attributed to Julius Richard Petri (1852-1921). In the latter part of the 19th century, Petri worked as a laboratory assistant for the renowned German scientist Robert Koch. Previous to the men's work, researchers cultured bacteria in broth. In 1881, Koch decided to try growing bacteria on solid media so he could more easily separate (and, more importantly, clearly observe and identify) different strains of bacteria in a single culture. He initially used gelatin spread on a flat piece of glass. However, in 1887 his assistant Petri made the advance of using a flat, coverable dish which they soon developed into the object we are familiar with today.
However, the dish may have been invented slightly earlier by a Slavonian scientist named Emanuel Klein (1844-1925) who did his research in England. Klein had written a then-influential textbook titled Micro-organisms and Disease. The third edition of the book was written in 1885 and contained a description of a dish nearly identical to the one Petri was supposed to have invented.
And as a further historical complication, another English researcher named Percy Frankland published a paper in 1886 in Proceedings of the Royal Society that described a very similar dish.
Whether it was a case of convergent technological evolution (which was common in the era) or whether Klein and Frankland were robbed of their proper place in science history by a more famous laboratory, we will probably never know.
Some of the information in this writeup was gleaned from http://www1.umn.edu/ships/updates/shadows.htm and http://www.socgenmicrobiol.org.uk/QUA/11_13.pdf; the rest was taken from the science dictionary at http://biotech.icmb.utexas.edu/; I oversaw the development of the dictionary (the website was mothballed in 1998) and I believe I wrote the entry this is based on.