what exactly means:implementation of spatial relational operators in databases?

Spatial databases are those that contain data about physical space - so that can either be geometric data which is in flat planes, or geographic data which is in curved planes, like the earth's surface.

The operators for those types of data are defined here for geography and here for gerometry. Because the two types of spatial data are implemented as CLR types in SQL Server, the operations on them are performed by the CLR type operators, both static (i.e. call them with typename::methodname) and instanced (i.e. call them with columnname.functionname).