Etymology of the term monilophyte

Monilophytes = Leptosporangiate ferns, horsetails, whisk ferns, marattioid ferns, & ophioglossoid ferns.

According to A Dictionary of Entomology:

Latin, monil = necklace

As for "phyte," I'll quote this Source:

Greek, -phyte = denoting a plant or plantlike organism

So it literally means "necklace plants. "

From Rai & Graham (2010) :

The extant monilophytes (a name based on a “moniliform” or necklace-like stele thought to be ancestral in the group; Kenrick and Crane, 1997; Pryer et al., 2004)

Note : stele = the central core of the stem and root of a vascular plant, consisting of the vascular tissue (xylem and phloem) and associated supporting tissue.

In other words, the vasculature of all of these plants are arranged like a beaded necklace. This is further alluded to in Pryer et al. (2004) as quoted in @Kendall's answer

Phylogeny and evolution of ferns (monilophytes) with a focus on the early leptosporangiate divergences:

The monilophytes (= Infradivision Moniliformopses, sensu Kenrick and Crane, 1997⇓) share a distinctive vasculature, having protoxylem confined to lobes of the xylem strand (Stein, 1993⇓), therefore the Latin moniliformis appellation for “necklace-like.”