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Speakers come in many shapes and sizes based on their needs. For the mobile phone there are smaller micro level speaker which are designed to produce clearer sound while bigger speakers are used where you need louder size for example in your home audio system. These days there are various kinds too. Like to produce bass sound you will need woofers. But all of them are based on same physics rules. The main function of speakers is to convert electronic signals into sound waves same as we produce sound while speaking. Or any other thing making a sound. Actually it produces soundwaves which strike over our eardrums and we are able to understand those sound waves.
Every speaker contains an electromagnet which converts electrical signal to audible sound. There is a metal coil inside speakers where actually current flows and it creates current in the coil flips the poles of magnet.
And electromagnet can be found in front of permanent magnet. The permanent magnet is firmly placed in its position and it does not move while electromagnet is mobile and it vibrates on based of its electronic signals.
When current flows through it the electromagnet changes its position or in other words it starts other words, it sometimes goes closer to the permanent magnet while sometimes it repelles from it according to electronic signals. This process happens in the matter of miliseconds.
The electronic magnet is than attached to a cone which is made with different kind of stuff according to need of the speaker. Sometimes it is made of paper and sometime it is made of plastic. But the main purpose of this cone is same. It amplifies the vibration of electromagnet which moves. So the cone does also vibrate with electronic magnet based on the electronic signal pulses. This cone then produces sound waves into air which strike towards your ears and sound is produced.
So inside a speaker there are three important things. First one is permanent magnet which actually does not move. And top of it is electromagnet which moves according to current pulses and the 3rd thing in speaker is its cone attached to electromagnet which amplifies the vibration of electromagnet to produce louder sound.
Microphone also uses the same principle but its inverse. Even you can use your earphones speakers as microphones.
These days to produce great quality sound, good speakers has different kind of cones embedded on one speaker to produce better, more quality and clearer sound.

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