There are usually 3 or 4 various types of filters fitted to mechanical engines that serve different purposes for the application that it’s being used for.
Some examples of filters are: 

Air Filters –

probably the most common in mechanical engines. They are used to stop dust, dirt and other air particles entering the engine, while allowing air in to engine for the combustion process. The engines air filter is very important and should be inspected and replaced or cleaned yearly depending on the environment the engine is being used in.

Oil filters –

These are the most important filter in an engines operation and longevity. During operation the engine heats up and with normal wear and tear will cause deposits of metal that need to be caught by the filter before they can build up and cause blockages or alter the performance of the engine. Generally you will need to change the oil filter every time you change the oil in the engine. They will generally be fitted directly to the engine bay and screwed in. 

Fuel Filters -

Depending on if the engine is petrol or diesel they will serve different purposes. Fuel filters in a petrol engine are generally used to stop impurities in the fuel that you put in the tank, stop any dirt that may have made its way into your fuel tank during re-fueling. There may be only one or several fuel filters that are positioned between the petrol tank and the engine.

Typically in modern cars there are two filters: 
1. One connected in the fuel tank at the end of the petrol tanks source before the fuel pump 
2. One that is connected between the fuel pump and the engine.

In a diesel engine the filters are used to prevent moisture building up in the engine, this is generally caused by condensation in the fuel tank, the filter is used to collect the water content, separate it from the Diesel in the fuel and remove it from the tank before it gets taken in to the engine.

Servicing the filters

Air Filters - Depending on the type of air filter, some can be cleaned and others will need to be replaced. K&N filters are usually the best choice as they have the ability to be taken off and cleaned they are made with 4-6 layers of premium cotton gauze which is then coated in wire mesh screen. They offer increased high air flow and usually come with a very long warranty. Generally other air filters are made of some type of paper which cannot be washed and will need to be replaced, have lower air intake and are prone to clogging more rapidly.