A mole is a unit of measurement in chemistry, which is used to count how much of a substance is present in a sample. The term was first used by Wilhelm Ostwald of Germany during the 1890s, who presumably intended it to be an abbreviation for "molecule" (or, in German, Molekul). Like most international standard (SI) measurement units, the system is useful despite having an essentially arbitrary "objective" base definition: in this case, one mole is equal to the number of atoms present in a sample of the carbon-12 isotope which weighs exactly 12 grams. The answer, according to reliable estimates, is about 602 sextillion (602 followed by 21 zeroes). However, "mole" can be used to refer to 602 sextillion atoms of any element, not just carbon: for example, a chemist could also speak confidently of a sample of one mole of oxygen, or six moles of iodine.
Key to the definition of the mole is the observation by chemists that samples of pure elements have reliable and predictable weights based on the masses of the atoms of that element. One mole of carbon-12 weighs 12 grams - which is useful to know because carbon atoms have twelve components of significant mass, six protons and six neutrons. An oxygen atom, by contrast, has 16 components of significant mass (eight protons and eight neutrons) - and so one mole of oxygen weighs 16 grams. The weight of a mole in grams is equal to the total number of protons and neutrons in the nucleus of the average atom in the sample - or, in the case of compounds, to the average total number of protons and neutrons in the nuclei of all the atoms making up each compound. This ratio is known as Avogrado's Constant and is highly useful in basic chemistry.
The usefulness of atomic weight, and its relation to the overall mass of a sample of that chemical, began in the late 1700s with the work of John Dalton. The realization that atoms had specific weights, at that time, allowed a useful coming-together of adherents of several different atomic theories: one could disagree about what precisely an atom consisted of, while still agreeing on what the atom weighed and on how it would generally behave when interacting with other chemicals. The beginnings of standardized mass measurements, which were eventually refined into the use of the mole, began in the 1800s with Jons Berzelius, who used oxygen as his base for measurement, and then Charles Gerhardt, who used hydrogen.