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The Praemonstratensian Abbey of St John the Baptist was founded in 1190s, by the de Moulton family. It was a house of the "White Monks", who as Canons undertook preaching and pastoral work in the area within the Cistecian rule of austerity.

Never a wealthy house, the foundation suffered in various wars between the Scots and the English.

Finally dissolved in 1540, the North and East of the Cloister were used as a Manorial house by Robert Strelley. The site came into the hands of John Morritt of Rokeby Hall who lived there from 1770 until a new hall was built at Rokeby. Some parts of the East range were still used to house estate workers until the late 1800s. The Morrit family passed the ruins to the state in 1925.

There is a lengthy description, and a list of the Abbots, in the Victoria County History for York. See Link

The site is a scheduled ancient monument (Link ) and a grade I listed building (Link ). The ruins are under the control of English Heritage (Link ). There is no charge for admittance.

In the United Kingdom, a scheduled monument is a 'nationally important' archaeological site or historic building, given protection against unauthorised change.
There are about 20,000 scheduled monuments in England representing about 37,000 heritage assets. Of the tens of thousands of scheduled monuments in the UK, most are inconspicuous archaeological sites, but some are large ruins.
Wikipedia: Link

Listed buildings and structures are officially designated as being of special architectural, historical or cultural significance. There are over half a million listed structures in the United Kingdom, covered by around 375,000 listings.
Listed status is more commonly associated with buildings or groups of buildings, however it can cover many other structures, including bridges, headstones, steps, ponds, monuments, walls, phone boxes, wrecks, parks, and heritage sites, and in more recent times a road crossing (Abbey Road) and graffiti art (Banksy 'Spy-booth') have been included.

In England and Wales there are three main listing designations;
Grade I (2.5%) - exceptional interest, sometimes considered to be internationally important.
Grade II* (5.5%) - particularly important buildings of more than special interest.
Grade II (92%) - nationally important and of special interest.

There are also locally listed structures (at the discretion of local authorities) using A, B and C designations.

In Scotland three classifications are also used but the criteria are different. There are around 47,500 Listed buildings.
Category A (8%)- generally equivalent to Grade I and II* in England and Wales
Category B (51%)- this appears generally to cover the ground of Grade II, recognising national importance.
Category C (41%)- buildings of local importance, probably with some overlap with English Grade II.

In Northern Ireland the criteria are similar to Scotland, but the classifications are:
Grade A (2.3%)
Grade B+ (4.7%)
Grade B (93%)

Read more at Wikipedia Link