What do astronomers consider a metal?
Astronomers consider any chemical element heavier than hydrogen a metal. This is because when the Universe began in the Big Bang the only elements produced in large abundances where hydrogen and helium (the two lightest elements). Stars produce all elements heavier than hydrogen in their cores as a result of the process of fusion by which they produce energy to shine. So all the chemical elements produced in stars are considered metals.
What is metallicity?
Metallicity is a measure of the amount of metals (as astronomers define metals) in an object of study. Most often astronomers use measurements of absorption lines in a stellar spectrum to measure the amount of iron present. Absorption lines due to hydrogen are analyzed in a similar manner to obtain the amount of hydrogen. The ratio of the amount of iron to the amount of hydrogen in the object is divided by the ratio of the amount of iron to the amount of hydrogen in our Sun to obtain a metallicity relative to the Sun. This value, denoted as [Fe/H] for that object, is plotted on a logarithmic scale. Therefore [Fe/H] = -1 denotes that the object of interest has 1/10th the amount of metals in it that the Sun has and [Fe/H] = +1 would denote 10 times the metal content of the Sun.
What do we learn from a star's metallicity?
Since all only hydrogen and helium (with very small trace amounts of Lithium and Beryllium) were produced at the beginning of the universe in the Big Bang, all of the iron and other metals in the universe have been produced in stars. At the end of a star's life, it recycles some or all of the elements it has produced in it's core over it's lifetime back into the interstellar medium. This processed material becomes mixed into clouds where the next generation of stars are born. So each subsequent generation of stars is enriched with the metals produced in previous generations. Because of this we can infer in a closed system, like our galaxy, that stars with a lower metal content (smaller [Fe/H]) are older than stars with a higher metal content (larger [Fe/H])
How is this useful when studying the structure of our galaxy?
Different parts of our galaxy have different metal contents so we can infer their relative ages, as well as use the [Fe/H] of a star to identify which population that star belongs to. For example, the halo is the part of the galaxy with the smallest amount of metals (the stars have an average [Fe/H] of -1.6 or about 30 times less iron than the sun). For this reason we believe that the halo may be the oldest part of the galaxy. Since the distribution of metallicities in the halo has a long tail towards more negative [Fe/H] values, we believe that the halo could have been the first part of the galaxy to form. The lack of stars with small metallicities in the disk of the galaxy lead us to believe that the disk was one of the last parts of the galaxy to form.