What is meant by "his swift foot"?

This sonnet addresses a theme which Shakespeare also deals with in many others: the idea of "sad mortality" and its singular potency over everything else on earth. In this sonnet, Shakespeare uses personification to intensify his imagery: beauty expresses a "plea" against mortality to spare her, but in the end, is powerless against the ravages of time.
It is time who is referred to, then, when the speaker decries "his swift foot." The feet of time, the speaker indicates, are moving very quickly; time progresses faster than we ever expect it to, and nobody is strong enough to slow it down or make it stop.
In the final couplet of the poem, the speaker suggests that there is only one way to perform the "miracle" of thwarting time and his destruction of all of us. By committing his love to "black ink," it can endure, even after both speaker and subject have been consumed by inevitable mortality.