It's a 33 bead rosary which takes it's design from both the Roman Catholic dominican and the Eastern Orthodox chotki (rope). The prayers are up to you in regards to what you pray on each bead. People do a lot of traditional ones on them, though. For instance, you start with the cross and open with the apostle's creed or the nicene creed, then the first bead (invitiatory bead) could be the Lord's Prayer, then the first cruciform bead is Gloria Patri, and the weeks will be the Jesus Prayer. Then you can return to the invitiatory after the first cycle and say the Trisagion, then to the cross again and say "In the name of the father, the son, and the holy spirit, amen." That is a common way to pray it, but you can assign scriptures to any of them. The whole point was to have a rosary that was not focused on prayers to Mary and the saints and was more compatible with Protestant doctrine.
They're usually called Anglican Prayer Beads, and were (I think?) invented in the 1980's. This is one of the standard sites about them: http://kingofpeace.org/prayerbeads.htm As you will see, there is no standard use for them, like the (Dominican) Rosary. There are tons of different set prayers that people have used and suggested for the different beads going around. I know a couple people who love them (orthodox Anglicans, not just touchy-feely people, among whom I can't help but suspect these beads originated), and they testify that they're particularly useful for "centering prayer" - that is, quiet meditation that pulls the attention away from the scattered worries of the world and onto Christ. Personally, I've gotten relatively little use out of them, though slightly moreso than the standard Dominican Rosary. I've used Anglican Prayer Beads to quiet my mind and try to focus on the calendar's outline of the Gospel (Nativity/Epiphany, Death/Resurrection, Ascension/Pentecost, Trinity/All Saints), I've tried approximating the Dominican Rosary, and (perhaps most successfully) I have used them for intercession through a list of people to pray for: https://leorningcniht.wordpress.com/2011/12/08/the-agnus-dei-as-intercession/
Archibald Campbell Knowles, The Practice of Religion I don't personally pray the Rosary but many find it helpful for various reasons.
Mat 6:7 But when ye pray, use not vain repetitions, as the heathen do: for they think that they shall be heard for their much speaking. When I was RC I was given a rosary at my First Communion, and I only used it a handful of times in 20 years (mainly at funerals when the priest led everyone in praying the rosary). When I became a Protestant, one of their teachings was that reciting the same prayer over and over by rote is an example of 'vain repetitions.' (The other thing that struck me as a Protestant was realizing that RCs pray 10 times as much to Mary on the rosary as to God!) All in all, I've not had an urge to pray any sort of rosary for many years. I most often pray from the heart and in my own words, and I trust that God has heard and will do whatever can be done (in keeping with His overarching plans and purposes) in response to my prayer.
I take the vain repetitions to be praying about how good you are kinda like in the prayer of the Pharisee and the tax collector.
The Puritans used the "vain repetition" argument against the Litany in the Prayer Book, too. While it is repetitive, it is not vain; each item on the litany is a distinct prayer request. The rosary and other prayer beads, meanwhile, are meditations, not discreet intercessions as such, and thus do not qualify for our Lord's rebuke in Matthew 6:7.
I'm probably thinking more of the 10 "Hail Mary" prayers per decade (definitely a prayer for intercession) of the RC rosary. I have to admit, I possess no familiarity with the prayers associated with the Anglican rosary.
The Anglican rosary has no prayers associated with it except what you make it, but the example I have is a popular preference for some people.
My favorite contrast of vain repetition vs. good repetition: 1 Kings 18:27-29: the pagans spend all day begging Baal to send fire from heaven while Elijah mocks their fruitless efforts. Luke 18:35-43: the blind man keeps crying "Jesus, son of David, have mercy on me!" and people tell him to shut up. But he keeps repeating himself until his prayer is answered.
I felt the same way. I've gained a greater appreciation for Mary, but still believe that the Roman Church too often creates the impression that Mary is to be worshipped.