The Microphone is the part of the radio you speak into. This can typically be a desktop mic or a handheld mic or just an alotted area on the front of the handheld radio. The mircophone takes in your voice and using a membrane converts it to electronic pulses. These pulses are then sent to the transmitter. for more information try this link: Microphone
The Tranmitter is the part of the Radio system that takes input from the mircophone
and adds it to a carrier wave through modulation (i.e. changing some property of the carrier wave in such a manner
as to send information)and sends it to the antenna for more specifics please look here: Transmitter,
The Reciever takes the signal from the antenna and seperates the signal or information (i.e. the modulation) from the carrier wave and then sends it to a speaker for more try here: Reciever  Demodulation
A speaker is simply a piece of equipment that takes an electric signal and converts it into sound. this is typically done using some sort of membrane that is electrically charged. Speaker
The Transceiver combines the functionality of the Transmitter and the Reciever into
one piece of equipment.
The piece of equipment shown below (a Dr635 2meter/440) shows how the 4 parts can be combined into a single unit.