In the late Roman republic, the cohort (of which there were between six and ten) became the basic tactical unit of the legions. The cohort was composed of five to eight centuries, each led by a centurion assisted by an optio, a soldier who could read and write. The senior centurion of the legion and commander of the first cohort was called the primus pilus (first spear), a career soldier and advisor to the legate. While every normal cohort was composed of five to eight centuries (normally six in secondus to decius cohorts), the one that was led by the primus pilus (the first) had about ten centuries, or 800 men. It also had a number of other staff, such as cooks, clerks, etc; that is, non-combatants.
Only eight officers in a fully officered legion outranked the primus pilus: The legate (lēgātus legiōnis), commanding the legion; the senior tribune (tribunus laticlavus); the Camp Prefect (praefectus castrorum); and the five junior tribunes (tribūnī angusticlāviī).
In contrast to a modern military organization, a centurion is analogous to a whole range of modern ranks. Ordinary century commanders would be equivalent to a modern army's Captains or Majors that have been commissioned from the ranks. The primus pilus with his senior staff role might be considered equivalent to a modern Lt Colonel (again gaining his promotion through the ranks).
The literal translation of "primus pilus" is "first spear."  According to the Oxford Latin Dictionary, the word "pilus" when used in this sense would relate to the Latin word "pilum," or "spear" in English.