The short answer is that prokaryotes are bacteria. Bacteria are unicellular - that is they are only ever one cell not lots of cells working together like in a human for example. Bacterial or prokaryotic cells are different in a number of ways from what are called eukaryotic cells - the cells that are found in plants, fungi and animals - and therefore ourselves.
The main difference between eukaryotic and prokaryotic cells lies in how the nuclear material (i.e. DNA) is organised in the cell. Eukaryotes have the DNA enclosed in a nucleus - surrounded by a double membrane with pores in it to allow communication with the cell cytoplasm. Prokaryotes on the other hand have their DNA floating free in the cytoplasm - it often takes the form of a single, wound up chromosome and possibly some small circular pieces called 'plasmids' as well.
In fact, the lack of any double membrane surrounded organelles (structures like the nucleus and mitochondria) is what characterises the differences between prokaryotic and eukaryotic cells.
No surprise then that evolutionary theory suggest the appearance of prokaryotes on the earth before that of eukaryotes. Interestingly, mitochondria and chloroplasts actually contain their own DNA in the form of plasmids and actually resemble prokaryotes as well, in that mitochondria and chloroplasts also have folded membranes and their own ribosomes.
So, what may have happened to cause eukaryotes to evolve was the invasion of a cell by prokaryotes that took up residence in a symbiotic (mutually beneficial) relationship with the cell.
Prokaryotes are unicellular and divide rapidly by mitosis (simple cell division to create two identical daughter cells). They may however connect (called conjugation) and exchange and recombine their DNA. Thus bacteria can become multiple resistant to antibiotics through mutation, rapid division and conjugation.
Prokaryotes cause diseases such as cholera and tuberculosis which afflict millions around the world. However genetically engineered bacteria that have had human genes inserted produce insulin for diabetics, human growth hormone and factor eight for hemophiliacs.
There are various types of prokaryotes - pathogenic ones that cause disease as mentioned above, also bacteria in the soil that convert nitrogen into a form that is available to plants, blue-green bacteria that photosynthesis, those that live in hot springs at temperatures above 90 degrees C. The list of different types goes on and on - bacteria mutate with great frequency and can adapt to almost any environment - antibiotic resistance is one example of this. This is partly down to the sheer number of bacteria and the rate they reproduce - one bacteria can give rise to billions within a day or two.
Prokaryotes then are bacteria, cells with a simpler organisation than our own, eukaryotic cells. Prokaryotes are very important in many aspects of Biology.