I have been on both the author and the referee sides, but I was wondering how editors approach their task. In particular, to what level of detail do you read the paper you assign to referees, and when (i.e. before or after receiving the reviews)?
From conversations with a mentor who was the editor-in-chief for a major journal, if you take the responsibility seriously, you need to have enough of an understanding of the papers assigned to you to figure out which referees will be suitable for a paper, while not taking so much time to read it that you can't process all of them for lack of time. As mentioned above, you need to at least a "high-level" read of the paper before assigning it to the referees. If the paper comes back with mixed reviews, it probably requires a careful re-read; if the reviews are uniform in recommending for or against publication, then it may not be as critical.
However, the editor will want to read papers when revisions come in, so that may mean going through a paper several times during the course of the review process.
In addition to the reply from aeismail to which I agree you need to add several other aspects. First, let's emphasise that good indepth knowledge of the field is vital.
The first stage for an editor is to assess whether the paper is appropriate for the journal, that it follows instructions for authors and is of reasonable technical quality to go to review (figures in order, language ok etc.)
The second stage for an editor is as was already stated to identify and assign referees based on the content of the papeer and reviewers speciality.
The third stage is to assess the reviewers comments and provide the author(s) with an educated summary of the reviewers work and possibly help by providing guidelines as to how to handle the reviews, emphasising some comments and possibly de-emphasising others. It not uncommon that reviews differ widely and in such cases the editor must be able to mediate, alternatively assign additional reviewers. This means apply objectivity and evaluate reviews. It also means you need to understand (at a deeper level) the paper and the comments that go with it.
The fourth stage concerns the revised work. Once the revised version is back from the author you need to evaluate the authors response to the reviewers comments. The author may not agree with the reviewers comments and it is the editors job to judge the revisons and make appropriate decisions (for additional review or accept/reject).
It might be appropriate to point out here that the editor is not just an evaluator but also a mediator. Disagrements between authors and reviewers are common. Some reviewers may have good points but terible ways of conveying them. In such cases the editor must place him/herself above the infected views and convey the essential points being made to the author.
The fifth stage concerns final decisions. This can be a formality but to have an editor sign off on a paper for publication means it has gone through peer review/revisions in a satisfactory way and is sound. So it is an important final step.