Why do reviews of articles often start with a summary of the article?
Reviews are communications to the editor, and an effective review tells the editor what the article is about (in that reviewer's opinion), using significantly fewer words than authors typically use. If an editor has to process a couple hundred submissions per year, it's not possible for him/her to carefully read every paper, so the editor will especially care if the reviewers agree on what the paper purports to show and whether the paper actually shows it.
I always start my reviews with a summary, as a way of establishing that I have understood the key ideas of the paper. I feel that this then places me on firmer ground in any subsequent praise or criticism.
I'll (cautiously) agree that this summary may be superfluous. In the best of all possible worlds, this exact information should be in the manuscript's abstract, which is at the editor's fingertips when he reads the review and makes a decision on the manuscript.
Sometimes, rarely, I find myself in this best of all possible worlds and find that I can't express the paper's contents in a better way than the authors did in their abstract. In such a case, I'll happily write
For the contents of the manuscript, see its abstract.
as the first paragraph of my review. (I then proceed to show that I actually did read the entire paper, by writing a clear and detailed review, and that this first paragraph is not laziness on my part. Writing a summary of the paper has a signaling function: it signals to the editor that you (a) actually read the paper, and (b) are not too lazy to summarize it.)
Usually, I find that (I think that) I can summarize the paper better than the abstract did - for instance, if the authors wrote a "teaser abstract", where they write what question they investigate but do not give their results, so people have to dig into the actual paper to find out what the results were. In such a case, I'll write such a summary, and usually recommend that the abstract be improved.
(EDIT) Here is what Jeff Leek, one of the bigger names in statistics writes on the topic in this highly recommended text on how he wants members of his group to review papers:
I think the summary is critical because if you can't distill the ideas down then you haven't really understood the paper. The summary should absolutely not be a restatement of the abstract of the paper, you should find the parts you think are most relevant and include them in the summary.