We investigate the formation and properties of low surface brightness galaxies (LSBGs) with $M_{*} > 10^{9.5} mathrm{M_{odot}}$ in the EAGLE hydrodynamical cosmological simulation. Galaxy surface brightness depends on a combination of stellar mass surface density and mass-to-light ratio ($M/L$), such that low surface brightness is strongly correlated with both galaxy angular momentum (low surface density) and low specific star formation rate (high $M/L$). This drives most of the other observed correlations between surface brightness and galaxy properties, such as the fact that most LSBGs have low metallicity. We find that LSBGs are more isolated than high surface brightness galaxies (HSBGs), in agreement with observations, but that this trend is driven entirely by the fact that LSBGs are unlikely to be close-in satellites. The majority of LSBGs are consistent with a formation scenario in which the galaxies with the highest angular momentum are those that formed most of their stars recently from a gas reservoir co-rotating with a high-spin dark matter halo. However, the most extended LSBG disks in EAGLE, which are comparable in size to observed giant LSBGs, are built up via mergers. These galaxies are found to inhabit dark matter halos with a higher spin in their inner regions ($<0.1r_{200c}$), even when excluding the effects of baryonic physics by considering matching halos from a dark matter only simulation with identical initial conditions.
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