The first coordination sphere refers to the molecules that are attached directly to the metal. The interactions between the first and second coordination spheres usually involve hydrogen-bonding.  For charged complexes, ion pairing is important.  
In hexamminecobalt(III) chloride ([Co(NH)]Cl), the cobalt cation plus the 6 ammonia ligands comprise the first coordination sphere. The coordination sphere of this ion thus consists of a central MN core "decorated" by 18 N−H bonds that radiate outwards.