Single supply amplifier biasing
(1) It is the task of the capacitor C1 to decouple the input signal source from the feedback path for DC as well as very low-frequencies. As mentioned, it forms the highpass BW2. Hence, it allows a fixed DC gain of unity and realizes a quiescent operating point at Vs/2 at the output.
(2) Therefore, for decoupling the amplified output signal from this DC-offset a coupling capacitor Cout is required (highpass BW3 )
(3) Without the capacitor C2 the common-mode noise appearing at the power-supply terminals would be amplified (because it appears also at the non-inv. opamp input). Therefore, it is the purpose of C2 to ground the midpoint between RA and RB (the non-inv. input) for frequencies above BW1. (Remember: For split supply this terminal is also connected to ground.)