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The term star formation history (SFH) often is used for the function or graph of star formation rate (SFR) over time. The concept of SFHs of galaxies is often used, as well as for other types of regions, e.g., the whole universe, galaxy clusters, stellar clusters, star-forming regions, etc. The graph would show SFR (or possibly the SFRD, star formation rate density) against years or redshift.
Such a history for a type of galaxy may be constructed by looking at the observed SFR of many examples over a long course of time. For individual nearby galaxies, such a history may be constructed by determining the age of individual stars (or collective stellar-age-population statistics derived from the electromagnetic radiation of the galaxy or regions within it) and extrapolating back to the star formation at the time the stars were born. Synthetic SFHs can also be produced by simulations, for comparison with those constructed from observation, to improve and/or confirm both the construction and the simulation.
A well-known type of plot showing the star formation history of galaxies over the entire history of the universe shows a rise to the peak star-formation epoch and subsequent fall.
The term star formation history is also naturally used in a more general sense, e.g., for other types of descriptions as well as the study of star formation over time, for the entire universe as well as more specifically for galaxy clusters, individual galaxies (notably the Milky Way, the study also referred to as galactic archaeology), and smaller groupings of stars such as stellar clusters.