Loose or wobbly
Over time toilets may become loose or wobbly. The first thing to check, is the bolts holding the toilet to the floor. Are they tight and if they have a washer and nut on them. Rusted and damaged bolts should be replaced with new ones.
Floor or toilet not level
If the floor is not level, the toilet may wobble back and forth or side to side a little. Generally a triangle shaped shim will correct this. Merely get the right thickness of a shim, trim it to fit and slide it between the base of the toilet and the floor.
Who to consult? Plumbers and qualified handymen.
Home owners usually can secure their toilet themselves, however, caution should be used so as not to over tighten. Plumbers and qualified handymen can easily do this work quickly and inexpensively.