This was an Ecclesiastical thing - i.e. Church Law.
Presentments were accusations of offences against Ecclesiastical law made by the wardens or chapter quest of each parish to the twice-yearly church courts held around Easter and November. Family historians will be familiar with them as a common crime presented, was that of fornication, as proved by the appearance of an illegitimate child, both mother and putative father, where known, were presented. Fornication was illicit sexual relationship by an unmarried party, adultery was an illicit relationship by a married party.