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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
• Understanding spatial relations