What does "Fe/H" mean?
"Fe" is the chemical symbol for iron, and "H" is the symbol for hydrogen. Thus, "Fe/H" is the ratio of iron to hydrogen. In practice, though, there is a bit more to the meaning.
Stars are made mostly of hydrogen. The first stars in the universe were thought to be made entirely of that element, before any other element existed, except helium. Helium is an exception, of course, because the moment stars are born, they start producing this element. Likely there are no pure hydrogen fields left in the universe. All stellar nurseries are likely tainted with heavier elements, some more than others. And, because of this, all newly born stars consist of hydrogen with a little chemical "flavoring."
Iron is only one of many elements that can appear in the spectrum of a star. Scientists are able to tell the relative abundance of the various elements in a star's atmosphere by measuring the star's spectrum. The abundance of each such element is compared to the relative abundance of hydrogen, and that ratio is then compared to a reference star, usually our own sun (Sol). Thus in practice, Fe/H refers to a ratio of a ratio.
To compress the scale of this comparison, scientists typically take the logarithm of such a ratio, thus creating a more "bite-size" number. Iron abundance for a star, as compared to the iron abundance of a reference star (say, our own sun), can fall in a wide range of possible values. One recent table included logarithmic values from -5.6 to 2.9 representing real values from 0.000002512 to 794.3 (or 10-5.6 to 102.9).
If you have a star with iron content equal to that of our sun, then the Fe/H is said to be zero. For example, the relative iron abundance for our own sun (when compared to itself) would naturally be 1.0 (ratio of 1:1), yielding an Fe/H of log10 1.0 = 0.0, i.e. zero difference.
Fe/HSol = 1.0,... Log10(1.0) = 0,... 100 = 1.0
For a star with small or "poor" iron content, the Fe/H might be something like "-3."
Fe/HPoor Star = -3.0,... Log10(0.001) = -3,... 10-3 = 0.001
And, for a star with large or "rich" iron content, the Fe/H might be something like "2.5."
Fe/HRich Star = 2.5,... Log10(316.2) = 2.5,... 102.5 = 316.2
Finally, we can say that Fe/H is the logarithm of the ratio, between two stars, of the ratio between iron and hydrogen abundances. That may be a mouthful, but Fe/H is an important term in the discussion of stars, their lives, and the likelihood that they might harbor planets.