Step 1: What the term means.
Mobility (\(\mu\)) measures the responsiveness of a charge carrier to an electric field. A carrier with high mobility drifts fast even in a weak field; a carrier with low mobility drifts slowly. It is a property of the material and the type of carrier.
Step 2: Write it as a ratio.
By definition it is the drift speed produced per unit field strength:
\[ \mu = \frac{\text{drift velocity}}{\text{electric field}} = \frac{v_d}{E} \]
Step 3: Connect to current density (a different framing).
The current density is \(J = nev_d\), and also \(J = \sigma E\) where \(\sigma\) is conductivity. Comparing, \(\sigma = ne\,(v_d/E) = ne\mu\). Hence mobility can equally be viewed through \(\sigma = ne\mu\), giving \(\mu = \dfrac{\sigma}{ne}\), where \(n\) is carrier number density and \(e\) the carrier charge.
Step 4: Unit.
From \(\mu = v_d/E\), the unit is \(\dfrac{\text{m s}^{-1}}{\text{V m}^{-1}} = \text{m}^2\,\text{V}^{-1}\,\text{s}^{-1}\).
\[\boxed{\ \mu = \dfrac{v_d}{E}\ }\]