In QED, the $\beta$-function has a positive sign. This means that the coupling increases at higher energies, or equivalently, smaller length scales. This picture is made intuitively clear by the following heuristic argument:
Consider the electron-positron loops in the photon propagator. These fluctuations screen charge in a vacuum, lowering the effective charge. As you move in closer, the charge is less screened, so the coupling should increase.
However, the opposite effect is true for an asymptotically free theory, such as QCD: The beta function is negative. As the length scale decreases, the coupling decreases How should one intuitively interpret asymptotic freedom? Is there a nice argument like the charge-screening picture for QED?