ST_Covers — Tests if every point of B lies in A
boolean ST_Covers(geometry 
      geomA, geometry 
      geomB);
boolean ST_Covers(geography 
      geogpolyA, geography 
      geogpointB);
Returns true if every point in Geometry/Geography B lies inside
            (i.e. intersects the interior or boundary of)
            Geometry/Geography A.
            Equivalently, tests that no point of B lies outside (in the exterior of) A.
            
In mathematical terms: ST_Covers(A, B) ⇔ A ⋂ B = B
ST_Covers is the converse of ST_CoveredBy.
    So, ST_Covers(A,B) = ST_CoveredBy(B,A).
Generally this function should be used instead of ST_Contains, since it has a simpler definition which does not have the quirk that "geometries do not contain their boundary".
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This function automatically includes a bounding box comparison that makes use of any spatial indexes that are available on the geometries. 
         To avoid index use, use the function   | 
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Enhanced: 3.0.0 enabled support for   | 
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Do not use this function with invalid geometries. You will get unexpected results.  | 
Performed by the GEOS module
Enhanced: 2.4.0 Support for polygon in polygon and line in polygon added for geography type
Enhanced: 2.3.0 Enhancement to PIP short-circuit for geometry extended to support MultiPoints with few points. Prior versions only supported point in polygon.
Availability: 1.5 - support for geography was introduced.
Availability: 1.2.2
NOTE: this is the "allowable" version that returns a boolean, not an integer.
Not an OGC standard, but Oracle has it too.
Geometry example
  --a circle covering a circle
SELECT ST_Covers(smallc,smallc) As smallinsmall,
  ST_Covers(smallc, bigc) As smallcoversbig,
  ST_Covers(bigc, ST_ExteriorRing(bigc)) As bigcoversexterior,
  ST_Contains(bigc, ST_ExteriorRing(bigc)) As bigcontainsexterior
FROM (SELECT ST_Buffer(ST_GeomFromText('POINT(1 2)'), 10) As smallc,
  ST_Buffer(ST_GeomFromText('POINT(1 2)'), 20) As bigc) As foo;
  --Result
 smallinsmall | smallcoversbig | bigcoversexterior | bigcontainsexterior
--------------+----------------+-------------------+---------------------
 t            | f              | t                 | f
(1 row) Geeography Example
-- a point with a 300 meter buffer compared to a point, a point and its 10 meter buffer
SELECT ST_Covers(geog_poly, geog_pt) As poly_covers_pt,
  ST_Covers(ST_Buffer(geog_pt,10), geog_pt) As buff_10m_covers_cent
  FROM (SELECT ST_Buffer(ST_GeogFromText('SRID=4326;POINT(-99.327 31.4821)'), 300) As geog_poly,
        ST_GeogFromText('SRID=4326;POINT(-99.33 31.483)') As geog_pt ) As foo;
 poly_covers_pt | buff_10m_covers_cent
----------------+------------------
 f              | t