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You can find a lot of good explanation around the net or on textbook.
I can give you a brief description you fully understand looking for a good reference you easily can find.
In few words Moore and Mealy are sequential systems: the outputs depend not only on the input (combinational systems) but also by the "state" the system assumed.
With sequential machine you create a sequence: something which changes in time, like a counter or a CPU (to execute an instruction a CPU resolves a sequence of elementary steps).
How can we build a sequential machine? depending on the state, we need a memory!
so you use inputs to control the memory. The memory output both controls the same memory input and the machine output. With such a feedback you realise a system whose evolution depends on the previous state.
If the output only depends on the state, we have a Moore machine.
If the output of the machine depends on both the state anc the input, we delas on Mealy machine.
A sequential machine job is represented with a diagram where the state is a circle, whereas the jump from a state to the next is drawn with an arrow.
In this diagram, if we want to describe the Moore machine, in the circles we also report the value for the output; on the arrows we only write the input confoguration which determines the next state.
A Mealy machine has a similar diagram, but the output configuration is reported on the arrows because it depends on the input and the state.