I see that some Muslims have prayer beads. What do we use them for? Is it similar to Christians using a Rosary? Is this a mandatory practice for all Muslims to use and have?
Its called Misbaha or Tasbih. Some people use them to keep count for Dhikr. For example if they wish to say "Alhamdulilah" a specific number of times, they will say it while pushing the beads, when they reach the end they will know they have said it equal to the number of the beads. It is not mandatory.
Shaykh Ul Islam Ibn Taymiyyah was asked concerning the recitation of the Quran while counting in Salah using prayer beads, is such prayer invalid?
He replied: If the intention of the questioner concerns enumeration of verses or Surahs, there is nothing wrong in it. (Fatawa Al-Kubra, Volume 2, Page 233)
It is not mandatory though.