I suppose it's possible that this exercise might have some purpose other than thinning the herd for eventual layoffs. It could, for example, be part of an attempt to improve efficiency by systematically reviewing everyone's daily workload. Such an effort would need to be carefully explained, however, to ensure honest and objective participation.
A guy called Duane begs to differ, slightly:
As a director who sometimes tasks individuals with tracking their time, the goal is generally not for me to see what they are doing. Rather, the goal is for them to see how productive they are (not) being. It usually works.
It is important to remember at a job that we are looking for accomplishments, not activity.
Though another commenter replys to this with:
Asking employees to start tracking their behavior has, in my experience, always registered in their minds as
a: a threat to their long term employment,
b: an indication that their management knows very little about what they do,
c: a waste of often valuable, even essential time, and
d: a source of stress.
You can see where Duane is coming from and, I suppose, applied sparingly and with an upfront explanation it might be useful. However, it seems from the comments that most places just seem to be applying it in order to be seen using yet another management tool, the results of which are hardly cared about by anyone, least of all the management.
Unless your time is billable, I can't really see the point and, to recast the second commenters point b, if the management don't already know what you're doing they aren't managing.
Slacktivist also has a fine post on Rosa Parks and how accidental heroes often need a little careful planning.