How to expand a textField in flutter looks like a text Area

All you need to do is set the maxLines variable when creating a TextField.
I have added the text field inside a Card widget so you can see the total area.

@override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text("Simple Material App"),
      ),
      body: Column(
        children: <Widget>[
          Card(
            color: Colors.grey,
            child: Padding(
              padding: EdgeInsets.all(8.0),
              child: TextField(
                maxLines: 8, //or null 
                decoration: InputDecoration.collapsed(hintText: "Enter your text here"),
              ),
            )
          )
        ],
      )
    );
  }