Dwarf irregular galaxies are classified as such because they are small and lack any regular structure. Many astronomers believe that dwarf galaxies, like some of the ones shown on this page, were the first systems to collapse and start forming stars in the early universe. They represent the building blocks from which more massive galaxies (spirals and ellipticals) were later formed through mergers and accretion.
Dwarf irregulars are similar in many ways to very young galaxies, but they are much nearer and easier to study. These galaxies seem to have consumed only a tiny percentage of their reservoir of gas. Their stars have a much lower fraction of heavy elements than does the Sun. These are all indications that only a few generations of stars have formed there over time. Current star formation is taking place at a fairly high rate in starburst episodes. All these characteristics make dwarf irregular galaxies the ideal local analogues to young galaxies from the early universe.
Below are several dwarf irregular galaxies that have been imaged by Hubble. The bottom two, the Large and Small Magellanic Cloud (LMC and SMC) are so close that the small field of Hubble's view can not observe the entire galaxy, but is able to view particular features within these neighboring galaxies. The images of the LMC and SMC are from ground-based telescopes that have a wider field of view than Hubble.