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St Alphege's was built around 1070 by Archbishop Lanfranc. It was rebuilt in the 12th century, and again in the 13th and 15th centuries. Among the interesting features is a late 15th century pillar, funded by a bequest from Thomas Prude. A brass coat of arms has been set into the pillar, with the inscription, 'Gaude Prude Thoma per quem fit ista columna.', which very loosely translates as 'Thomas Prude paid for this column'.
Thomas Cushman was married at St Alphege's. Cuchman was responsible for hiring the Mayflower, the ship which took the Pilgrims to America in 1620. Cushman himself followed in 1621, but eventually returned to Britain, and died in Canterbury in 1625.
St Alphege ceased being used as a church in 1982, and for some time served as the home of the Canterbury Environmental Centre. It is now used by King's School, and the interior is not generally open to the public.
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