Generally, If there is a change in state or props values, React component always re-renders the component every time. A pure component is a component that checks whether the state and props values change or not and decide whether to re-render the component or not. That way we improve the application performance.
I will take an example to show you pure component:
I created a component Counter.js and ChildComponent.js and imported ChildComponent in Counter Component.

import {useState} from 'react'

import ChildComponent from './ChildComponent'

const Counter = () => {

    const [count,setCount]=useState(0);

  return (

    <>

    {count}

    <button onClick={()=>setCount(count+1)}>Increase</button>

    <ChildComponent/>

    </>

  )

}

export default Counter

import React from 'react'

const ChildComponent = () => {

    console.log('I am a child component');

  return (

    <div>ChildComponent</div>

  )

}

export default ChildComponent

and now the problem is when Counter Component change the count state ChildComponent also re-render. But ChildComponent didn't change any state or props.

So Pure Component reqired in ChildComponent. 

We will use memo to make ChildComponent  to make Pure Component.

import React,{memo} from 'react'

const ChildComponent = () => {

    console.log('I am a child component');

  return (

    <div>ChildComponent</div>

  )

}

export default memo(ChildComponent)

Now it will work perfect.