What is the meaning behind this chant?
It's taken from (or quoted in) MN 7 (but it's one of the Pali Formulae -- buddha-vacana.org says, of this one, "45 occurrences", so I suppose this occurs in 45 suttas; also, that it's a component of the Sekha Paṭipadā).

It's one of the Anussati -- specifically Saṅghānussati. Sati is "mindfulness" -- and anu is "after (behind)", "for (towards an aim)", "according to (in conformity with)", also "each/every/one-by-one" -- so, combined, "remember" or "recollect" or "call to mind".

AN 3.70 says (of all the Anussati) that, "as they recollect ... their mind becomes clear, joy arises, and mental corruptions are given up".

Commentary says that this is referring to the "ariya sangha" (the noble sangha), i.e. all enlightened ones. The "8 [types of] individuals" refer to the "four stages of enlightenment" (sotāpanna etc.) or as it says "the four pairs of persons" -- both ordained and/or lay.