Answer :

There are many different reasons for species becoming extinct: 

- They may be hunted to extinction by predators. See the Dodo for more information on this. 

- Their have to compete with 'foreign' species for food or habitat. This happens on many small islands when new predators are introduced. See rats and cats introduced to Hawaii by sailors. 

- They may require very specialised living conditions which dissapear due to a changing environment. 

- Disease or inbreeding reduces their numbers to unsustainable levels. 

- An outside event may create a catastrophic situation. See the meteor that caused the extinction of the dinosaurs. 

It matters because we are all part of the Earth's ecosystem. Imagine all plants and animals on earth linked together in a giant 'web'. Plants are eaten by insects. They are then eaten by larger animals which are in turn eaten by humans. As humans we are at the top of the food chain so may not notice too much as we can eat a lot of different foods. However other may animals depend on very specific prey. Extinction of a species is like removing a section from the 'web'. It has a knock-on effect on everything linked to it. 

Also from a different viewpoint, biodiversity (many different species) of the Earth makes the place interesting. It may not affect our ability to survive if species become extinct, but the world would become a lesser place and slightly less entertaining.
there are lots of different reasons y