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• intersects if the intersection of both geometries is not empty

• contains if the second geometry id completely contained into the first one

• disjoint if the intersection of both geometries is the empty set

• equals if they are spatially identical

• touches if the only points in common between both geometries lie in the union of their boundaries

• overlaps if the intersection of both geometries results in a value of the same dimension of both geometries and is different from both the first and the second geometry

• within if the first geometry is completely contained into the second one

• crosses if the intersection of both geometries results in a value whose dimension is less than the maximum dimension of both geometries and the intersection value includes points interior to both geometries, and the intersection value is not equal to either the first or the second geometry

References:

• 4.2 Evaluating relationships between geometries
• OpenGeo Suite | Working with your data | Data storage and management in PostGIS | Spatial relationships
• How Spatial Join Works in GIS
• Understanding spatial relations