To explain what exactly a subfloor is before actually mentioning the different types suited towards floor tiling, it is basically the floor which cannot be seen from which the visible top flooring is attached to, and in turn the subfloor is attached to the main solid flooring of your room.
Like a slice of cheese between two pieces of bread, the subfloor can be anything from underlay for carpet floorings, to solid cement and wire mesh based flooring between existing hardwood planks and floor tiles.
In a basement for example, if you were to look upwards to see an unfinished ceiling, this may be wooden planks mounted over joists that would account for your main flooring in the above room.
If it were a bathroom or kitchen, then a necessary solid subfloor would have to be installed prior to floor tiling in order to completely seal the wooden floor against water seepage into the basement, and to also prevent shifting of the tiles due to expansion and contraction of the wood when exposed to various climates, temperatures, and moisture.
If your floor tiling subfloor is not installed correctly against the main flooring, then cracks may appear in your finished grouting or the actual floor tiles, therefore it is important to do this correctly either it will make or break your finished floor tiling project.
Beginning with the option of plywood subfloors which are not so commonly used nowadays, these can be somewhat expensive due to the escalating cost of timber products, and with wood being prone to expansion/contraction.
As a general rule for floor tiling, when installing a plywood subfloor, the overall thickness of the main wooden floor and plywood subfloor should be no less than 1-1/4" inch thick.
At a rough guess, if your existing floor was say 3/4" inch thick, then you would require sheets of 1/2" inch plywood to bring the full thickness to 1-1/4" inch at minimum, but to be safe it would be better to install 3/4" inch plywood to bring the overall thickness to 1-1/2" inch.
The plywood you should use should be of construction grade for indoor-use only, as with outdoor-use plywood it has usually been pressure treated with various chemicals that you don't really want lingering about your home.
When laying it also, be sure and place the rough unfinished side facing upwards, as this will give a better surface for which your floor tile mortar to attach itself to.
When laying your sheets of plywood, these should be attached to the existing wooden flooring with the use of woodscrews, but as a guide for screw placement, you should first draw out a grid on the sheets no matter their size to ensure a true and positive attachment.
This pattern should basically be one screw every 4"inches around the outside edge of the plywood starting from each corner.
Then working towards the centre of the sheet, one screw every 8" inches inward from every second of the outside screws.
The outside screws should also be placed at least 1/2" to 3/4" inch inward from the edge to prevent the top ply from splitting and producing annoying upward splinters when screwing in the wood screws.
Pre-drill these markings if you wish to make attachment of the screws simpler, but if you do, make sure that your drill bit is of narrower diameter than the screw you are using.