I haven't done much on Probate this early on. But the key is the word Administration - which means that the person concerned died without a Will and therefore the Court had to appoint administrators to deal with his estate and so on.
My textbook tells me that the Act Book in the National Archives will usually have:
Date of grant of administration
Name of the intestate deceased
Parish of residence
Name of administrator and relationship to the intestate
Deadlines by which inventory and accounts had to be done
This isn't online and needs a visit to the National Archives or a researcher. Just to add to your luck, this particular date (1651-60) is in English - otherwise it would be Latin!
Now there might be more, according to my textbook the further items may well not be indexed or ou may need a paper catalogue at TNA. In series PROB16 you might find Court orders for distribution of the estate; in PROB2 you will find inventories, searchable online; Cause Papers in PROB1 searchable online.
This link might well help:
http://www.nationalarchives.gov.uk/records/research-guides/wills-and-probate-records.htmI'm sorry not to be as helpful as I'd like.
I recommend: "Tracing your ancestors in the National Archives" by Amanda Bevan; "Wills and other Probate Records" by Karen Grannum and Nigel Taylor, both published by TNA.