Work in ordered motion — steps with a direction, a beginning that intends its end. As a verb, to carry a thing through those steps.
Latin processus (a going forward, advance, progress), from procedere (to go forward): pro- (forward) + cedere (to go, to yield); a process is motion with a direction built into its own name.
Work moving in ordered steps toward an intended end. The root's own sense — a going-forward — is exactly the promise the word still keeps: a process is not just activity, it is activity with a direction.