For scientists, publication in a peer reviewed journal is the primary way of communicating experimental results, so getting a manuscript through the review process and into publication in a timely manner is important. This can get complicated if you are also trying to be published in the most prestigious journal possible.
For example, a scientist could submit their manuscript to a prestigious journal like Nature or Science. The article is sent out for review and within a few months (maybe faster) the authors get a note back saying that while their science was methodologically sound, it just wasn't innovative enough for those journals. Next, the scientist submits it to the top journal in their field, only to be told in a few months that it was too interdisciplinary for that journal. A scientist may go through several rounds of submission and rejection looking for a suitable home for their manuscript, worrying as the months slip by that someone else has beat them to the publication of similar results.
This submission and rejection takes time and energy from authors, editors and reviewers when they could use that time researching or teaching. The process is widely considered to be inefficient.
Enter the folks behind new "portable peer review" services. Traditionally, the review process was done within the organizational structure of the journal you submitted your manuscript to. These new services are independent of specific journals and their goal is to cut down on the redundant work being done in the publication process. This separates the review process from the publication process, (one version of the decoupled journal described by Priem and Hemminger, 2012). Companies like Rubriq, Peerage of Science and Science Open Reviewed want authors to take their reviews with them as they search for an appropriate publication venue.
While the details vary widely, it is similar to traditional journal based peer review. An author submits a manuscript, reviewers are located, and the reviewers provide commentary on the paper. The portable peer review services have generally taken the time to develop detailed rubrics and detailed guiding questions for reviewers. The authors can then revise their manuscripts and take everything to a journal of their choice. The portable peer review services are also working hard to cooperate with journal editors, allowing them to tell their authors that reviews from their service will be welcomed at specific journals. Some journals have instituted polices accepting outside peer review, like Elsevier's Virology journal. Virology is starting to welcome manuscripts that have been rejected by higher impact journals if they include the original reviews, a revised manuscript and the author's rebuttal in their submission package. BMC Biology, eLife, Biology Open, PLOS and EMBO are also cooperating and allowing authors to take their reviews with them.
Subscription journals have often mentioned that the management of the peer review process is one of the "value added" services that makes them worth the high costs. The portable peer review services have a variety of options for supporting themselves. Rubriq relies on author fees, right now around $600 per article (it is worth noting that Rubriq pays its reviewers). Peerage of Science is supported by several European universities and journal partners but does not charge author fees (nor does it pay reviewers). Science Open Reviewed helps connect authors and reviewers, allowing them to negotiate reviewing fees if they choose and is supported by Queen's University in Ontario, CA.
Importantly, these services often mention the desire to develop a "reputation economy" for reviewers. While many reviewers take the time to provide polite, constructive criticism of a manuscript, there are others who may simply say "this sucks." Knowing who is more likely to provide the former ahead of time could be useful. For example, Peerage of Science offers a "peer review of peer review" that rates reviewer reviews, and provides reviewer scores on reviewer profiles.
Although scientists recognize that peer review has problems, most recognize that it serves a valued role in communicating scientific research. New portable peer review services hope to improve the quality of reviews while simultaneously reducing the amount of redundancy in the publication system.
Priem, J., & Hemminger, B. M. (2012). Decoupling the scholarly journal. Frontiers in Computational Neuroscience, 6. Available from: http://dx.doi.org/10.3389/fncom.2012.00019