In summary the PCCs are responsible for...
Co-operating with the Rector in promoting the whole mission of the church: pastoral, evangelistic, social and ecumenical.
Managing the finances of the church and caring for the church buildings, areas which are delegated to subcommittees
Liaising with the higher councils of the Church of England through their representation on the Deanery Synod, and participating in diocesan funding through the Parish Share.
More detail of the responsibilties of PCC members can be found here
St Matthew's Harwell and All Saints' Chilton together form a Joint Benefice, the work of which is facilitated by regular meetings of the Combined PCC, where members of the two PCCs come together to discuss matters that are common to both parishes.
Churchwarden responsibilities can be found here