I know why we need diffuse and bump but not specular or displacement
I personally think it makes only a slight change.

Also? Is there any more important map?

all the material layers are there to give you more control over your textures and how they are displayed on your model. you may want to add a specular map for controlling the highlights on your material, something you may not be able to achieve with modifying just a diffuse map. you may want an opacity map for making things transparent, or a reflect map to control how your material is reflecting or an environment map to control what is actually shown in the reflection etc.

so in conclusion all of these are for added control to your materials, you can start to achieve some very photorealistic results when you start playing with all these material layers.

website: http://www.all3dmax.com

You don’t need to use all of the maps all of the time, and no one will force you to. But they each have their purpose in creating realistic materials.
For example the Specular map could be used to create an irridecent effect, where highlights are different colours. With a greyscale map in specular the intensity of the highlight is controlled for a material where some bits are shinier than others. Likewise mapping Glossiness can give a grimy, unpolished look to a material, more like real life than the perfect clean CGI world.
While Bump mapping is OK for fine surface details, is just a shading illusion, the geom doesn’t alter, so it won’t work for more extreme uneven surfaces, Displacement will, without the need to model such complex geometry.

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