  We present a detailed study of the rest-optical (3600-7000 Angstrom) nebular
spectra of ~380 star-forming galaxies at z~2-3 obtained with Keck/MOSFIRE as
part of the Keck Baryonic Structure Survey (KBSS). The KBSS-MOSFIRE sample is
representative of star-forming galaxies at these redshifts, with stellar masses
M*=10^9-10^11.5 M_sun and star formation rates SFR=3-1000 M_sun/yr. We focus on
robust measurements of many strong diagnostic emission lines for individual
galaxies: [O II]3727,3729, [Ne III]3869, H-beta, [O III]4960,5008, [N
II]6549,6585, H-alpha, and [S II]6718,6732. Comparisons with observations of
typical local galaxies from the Sloan Digital Sky Survey (SDSS) and between
subsamples of KBSS-MOSFIRE show that high-redshift galaxies exhibit a number of
significant differences in addition to the well-known offset in log([O
III]/H-beta) and log([N II]/H-alpha). We argue that the primary difference
between H II regions in z~2.3 galaxies and those at z~0 is an enhancement in
the degree of nebular excitation, as measured by [O III]/H-beta and R23=log[([O
III]+[O II])/H-beta]. At the same time, KBSS-MOSFIRE galaxies are ~10 times
more massive than z~0 galaxies with similar ionizing spectra and have higher
N/O (likely accompanied by higher O/H) at fixed excitation. These results
indicate the presence of harder ionizing radiation fields at fixed N/O and O/H
relative to typical z~0 galaxies, consistent with Fe-poor stellar population
models that include massive binaries, and highlight a population of massive,
high-specific star formation rate galaxies at high-redshift with systematically
different star formation histories than galaxies of similar stellar mass today.
