For those not familiar with the arXiv, it is a preprint server service that is free (expenses footed by multiple institutions around the world, notably Cornell University in the USA.) Researchers upload their preprints generally about the time that they submit the article for consideration for publication at a typical (eg. primarily dead-tree) journal. The article will be considered, accepted, rejected, modified etc. by the journal, which has generally asked other academics to review it (for free, motivated by a sense of community, typically) and then sometimes the author makes changes and gives the final version to the journal. They may or may not update the arXiv posting to reflect the changes (typos, revisions, serious issues) that have been made in response to the reviewing process. In any case, most of the people actually interested in the result will have long seen the arXiv posting long before the journal publication happens, so the journal is principally playing the role of a validator about importance, significance, originality, correctness, etc. rather than dissemination, for those who submit their work to the arXiv.
Different disciplines have different levels of participation in the arXiv; high-energy physics and many areas of math generally have broad participation, whereas computer science, statistics, and other areas in math have lower overall levels and different publishing culture.
What the Epijournals are a project to have the validation process be similar, but not to bother with the actually having a (primarily dead-tree) journal. Rather, they will be overlays to the arXiv so the hosting and logistical expenses are all already sorted out. There are multiple free electronic journals, but the costs associated with archiving, etc. are generally either borne from "page charges" to authors, various institutional support options, or private generosity. See for example the Electronic Journal of Combinatorics a long-standing top journal in combinatorics. With the hosting on the arXiv, this should remove one of the barriers to entry for new journals.