How can the SI unit of resistivity [Ωm] be interpreted?
\$\Omega\$m is the simplified unit of resistivity. The full unit is \$\Omega \$m\$^2/\$m. This means that a given length of material with a given cross sectional area will have a certain resistance whose value can be calculated using the resistivity.

For a 1 m length of material with a 1 mm\$^2\$ cross sectional area and a resistivity of 1:

\$1 \Omega \mathrm{m} = R(10^{-6}\mathrm{m}^2/1\mathrm{m})\$

\$R = {1\Omega \mathrm{m} \over(10^{-6}\mathrm{m}^2/1\mathrm{m})}
= 10^6\Omega\$