What the collection isI'm just going to quote directly from the National Archives for this bit:
The series of Ancient Petitions draws together a large number of petitions addressed to the king, to the king and council, to the king and council in parliament, to the chancellor, and to certain other officers of state.
The earliest petitions date to the reign of Henry III, and the latest example has been identified as belonging to the reign of James I. The vast majority of the petitions date to the period between the late thirteenth century and the middle of the fifteenth century; there is a particular concentration of documents which date to the reigns of Edward I, Edward II and Edward III. The majority of petitions are written in Anglo-Norman French, although some early examples are written in Latin, and English was used increasingly as the fifteenth century progressed.
The majority of petitions were presented by named individuals (both men and women), singly or in groups. Although there are examples of petitions presented by members of the peasantry, most petitioners tended to be members of the gentry, the nobility, the urban elites and the higher clergy. In addition to petitions presented by individuals, a significant number of cases were presented in the name of communities and corporations: many examples exist of petitions presented by villages, towns, ecclesiastical institutions and mercantile associations. There are also petitions which claimed to speak in the interests of the whole realm, and were accordingly addressed from the 'commons' or 'people'. Most of the petitions came from individuals and communities within England, but a significant minority were from other lands, especially Wales, Ireland, Scotland, Aquitaine and other parts of France.
Why is it useful?
The quick answer is that the entire set has been digitised and is freely viewable via the UK National Archives Discovery catalog. This means we can examine the original records easily and no charge.
It's usefulness within the SCA context is for English (mostly) naming patterns in a period before parish records. The only other commonly digitized record sets tend to be wills and they are relatively sparse even when they have been scanned, and not freely available, either charged at £3.50 at the UK National Archives or on sites like Ancestry requiring a subscription.
The names available cover people, places, objects and some animals. Boats are well represented as there seem to be a lot of disputes regarding sharp practice and plain piracy. Inn names are poorly represented. I think it reflects a pattern that inns may not have been widely named at this point, but I haven't rigorously investigated this. You will find numerous variant spellings. As an example, the entirety of my documentation on compound locatives and double locatives was from this series of records (and this a decade ago).