Giant H ii regions (GHIIRs) in nearby galaxies are a local sample in which we can study in detail processes in the interaction of gas, dust and newly formed stars which are analogous to those which occurred in episodes of higher intensity in which much of the current stellar population was born. Here, we present an analysis of NGC 588, a GHIIR in M33, based on optical Integral Field Spectroscopy data obtained with the Potsdam Multi-Aperture Spectrophotometer at the 3.5-m telescope of the Calar Alto Observatory, CAHA, together with Spitzer infrared images at 8 and 24 μm. The extinction distribution measured in the optical shows complex structure, with three maxima which correlate in position with those of the emission at 24 and 8 μm. Furthermore, the Hα luminosity absorbed by the dust within the H ii region reproduces the structure observed in the 24-μm image, supporting the use of the 24-μm band as a valid tracer of recent star formation. A velocity difference of ∼50 km s−1 was measured between the areas of high and low surface brightness, which would be expected if NGC 588 were an evolved GHIIR. We have carefully identified the areas which contribute most to the line ratios measured in the integrated spectrum. Those line ratios which are used in diagnostic diagrams proposed by Baldwin, Phillips & Terlevich (i.e. the BPT diagrams) show a larger range of variation in the low surface brightness areas. The ranges are ∼0.5–1.2 dex for [N ii]λ6584/Hα, 0.7–1.7 dex for [S ii]λλ6717,6731/Hα and 0.3–0.5 dex for [O iii]λ5007/Hβ, with higher values of [N ii]λ6584/Hα and [S ii]λλ6717,6731/Hα, and lower values of [O iii]λ5007/Hβ in the areas of lower surface brightness. Ratios corresponding to large ionization parameter (U) are found between the peak of the emission in Hβ and the main ionizing source decreasing radially outwards within the region. Differences between the integrated and local values of the U tracers can be as high as ∼0.8 dex, notably when using [O iii]λλ4959,5007/[O ii]λλ3726,3729 and in the high surface brightness spaxels. [O ii]λλ3726,3729/Hβ and [O iii]λλ4959,5007/[O ii]λλ3726,3729 yield similar local values for the ionization parameter, which are consistent with those expected from the integrated spectrum of an H ii region ionized by a single star. The ratio [S ii]λλ6717,6731/Hα departs significantly from the range predicted by this scenario, indicating the complex ionization structure in GHIIRs. There is a significant scatter in derivations of the metallicity using strong line tracers as a function of position, caused by variations in the degree of ionization. The scatter is smaller for N2O3 which points to this tracer as a better metallicity tracer than N2. One interesting result emerges from our comparison between integrated and local line ratio values: measurements of the line ratios of GHIIRs in galaxies at distances ≳25 Mpc may be dominated by the ionization conditions in their low surface brightness areas.