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Burlington House is on Piccadilly. It was originally a private Palladian mansion owned by the Earl of Burlington, and was expanded in the mid-19th century after being purchased by the British government.
Burlington House is most familiar to the general public as the venue for temporary art exhibitions from the Royal Academy, which is housed in the main building at the northern end of the courtyard. Five learned societies occupy the two wings on the east and west sides of the courtyard and the Piccadilly wing at the southern end. Collectively known as the Courtyard Societies, these societies are:
Geological Society of London (Piccadilly/east wing)
Linnean Society of London (Piccadilly/west wing)
Royal Astronomical Society (west wing)
Society of Antiquaries of London (west wing)
Royal Society of Chemistry (east wing)
Grade II* listed. 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