A Review Editor is a relatively low-stakes position, particularly if the journal already boasts some degree of prestige. Most journals publish various genres of scholarship. The title here refers to one of the lesser-known classifications of peer-reviewed publication: book reviews.
In similar fashion, academic conferences comprise various kinds of panels and time slots. You may be invited to share your extensive and fascinating original research in a ninety-minute panel discussion wherein you are the sole presenter. Or you may be accepted to the conference in combination, grouped into a panel with three other academics whose research aims match yours, or because your various conclusions seem to inform one another, or because all four of these hypothetical research efforts will likely appeal to a common audience segment (for example, an analysis of a budding marijuana industry may fit nicely paneled together with an exploration of the hidden meaning in children's cartoons). Some dedicated scholar will accept an offer to keynote the event, an honorary and certain center of attention. And some presenters will merely stand in the hallway with posters that compress their meaningful researches into two thousand square inches.
For peer-reviewed journals, book reviews are the poster boards of our publication-dependent life. Some scholars publish original research; others synthesize previous scholarship, often applying common wisdoms from earlier eras in analysis of some recent event or phenomenon. Some scholars read lengthy academic texts from other scholars--noticed works that show early indication of high impact--and review the book along a pretty standard range of criteria. The review editor (typically there's only one) offers copy edit and review for these submissions and recommends a certain number of them for inclusion in the journal's upcoming volume. (I hope no former or current reviewers of academic texts feel slighted here; I certainly intend no insult.)
Of course, your question was, "Is a master's student ready...?"
I suppose that depends on the student. I've met more than one instructor who began teaching university courses before completing undergraduate study. (No, seriously. Singly-assigned as instructor of record and paid a lecturer's wage.) If this response has helped you garner a sense of what you'd be stepping into, and if that doesn't sound dull, or terrifying, or somehow jointly meaningful and thankless, then give it a go. Sometimes I worry I'm too afraid of not winning some award or notoriety at a task and I let thoughts of prestige or career steal away interesting opportunities.
If it were me, I'd take it. I don't think I would spend too much time considering the offer an honor, but I think I could probably collate the reviews of impressive books and assess them according to a rubric that's already been hashed out for me. Then I'd see if I could somehow parlay it into earned credit toward my degree.