lifecycle event state and prevState in react.js

Here is a demo with a commented-out code to give you more information: http://codepen.io/PiotrBerebecki/pen/rrGWjm

1. What is state in line 3? that look like a global variable, it make
sense if it has var or const before it. Is that a lifecycle
function/var?

state in line 3 is just a property of the Counter component. Another way of initialising a state in React using ES6 syntax is as follows:

constructor() {
  super();
  this.state = {
    value: 0
  }
}

React docs: https://facebook.github.io/react/docs/reusable-components.html#es6-classes

The [React ES6 class] API is similar to React.createClass with the exception of
getInitialState. Instead of providing a separate getInitialState
method, you set up your own state property in the constructor.

2. Do I have to import Component from react? I remember I
need not to do that in v15.

You can alternatively just import React and define a class in the following way:

import React from 'react';

class Counter extends React.Component {
...

The below would also allow you to use Component API:

import React, { Component } from 'react';

class Counter extends Component {
... 

3. Where does prevState come from?

The prevState comes from the setState api: https://facebook.github.io/react/docs/component-api.html#setstate

It’s also possible to pass a function with the signature
function(state, props). This can be useful in some cases when you want
to enqueue an atomic update that consults the previous value of
state+props before setting any values. For instance, suppose we wanted
to increment a value in state:

this.setState(function(previousState, currentProps) {
  return {
     value: previousState.value + 1
  };
});

You will often see developers updating state in the following way. This is less reliable than the above method as state may be updated asynchronously and we should not rely on its values for calculating the next state.

 this.setState({
   value: this.state.value + 1 // prone to bugs
 });

Full code from my codepen:

class Counter extends React.Component {

  // state = { value: 0 };

  // you can also initialise state in React
  // in the constructor:
  constructor() {
    super();
    this.state = {
      value: 0
    }
  }

  increment = () => {
    this.setState(prevState => ({
      value: prevState.value + 1
    })); 
  }

  decrement = () => {
    this.setState(prevState => ({
      value: prevState.value - 1
    }));  
  }

  render() {
    return (
      <div>
        {this.state.value}
        <button onClick={this.increment}>+</button>
        <button onClick={this.decrement}>-</button>
      </div>
    )
  }
}


ReactDOM.render(
  <Counter />,
  document.getElementById('app')
);