  We analyze the sources of free electrons that produce the large dispersion
measures, DM $\approx 300-1600$ (in units cm$^{-3}$ pc), observed toward fast
radio bursts (FRBs). Individual galaxies typically produce DM $\sim 25-60$
cm$^{-3}$ pc from ionized gas in their disk, disk-halo interface, and
circumgalactic medium. Toward an FRB source at redshift $z$, a homogeneous IGM
containing a fraction $f_{\rm IGM}$ of cosmological baryons will produce DM $=
(935~{\rm cm}^{-3}~{\rm pc}) f_{\rm IGM} \, h_{70}^{-1} I(z)$, where $I(z) =
(2/3 \Omega_m)[ \{ \Omega_m(1+z)^3 + \Omega_{\Lambda} \}^{1/2} - 1 ]$. A
structured IGM of photoionized Ly-alpha absorbers in the cosmic web produces
similar dispersion, modeled from the observed distribution, $f_b(N,z)$, of H I
(Lya-forest) absorbers in column density and redshift with ionization
corrections and scaling relations from cosmological simulations. An analytic
formula for DM($z$) applied to observed FRB dispersions suggests that $z_{\rm
FRB} \approx 0.2-1.5$ for an IGM containing a significant baryon fraction,
$f_{\rm IGM} = 0.6\pm0.1$. Future surveys of the statistical distribution,
DM($z)$, of FRBs identified with specific galaxies and redshifts, can be used
to calibrate the IGM baryon fraction and distribution of Ly-alpha absorbers.
Fluctuations in DM at the level $\pm10$ cm$^{-3}$ pc will arise from filaments
and voids in the cosmic web.
