[javascript] What do multiple arrow functions mean in javascript?

Understanding the available syntaxes of arrow functions will give you an understanding of what behaviour they are introducing when 'chained' like in the examples you provided.

When an arrow function is written without block braces, with or without multiple parameters, the expression that constitutes the function's body is implicitly returned. In your example, that expression is another arrow function.

No arrow funcs              Implicitly return `e=>{…}`    Explicitly return `e=>{…}` 
---------------------------------------------------------------------------------
function (field) {         |  field => e => {            |  field => {
  return function (e) {    |                             |    return e => {
      e.preventDefault()   |    e.preventDefault()       |      e.preventDefault()
  }                        |                             |    }
}                          |  }                          |  }

Another advantage of writing anonymous functions using the arrow syntax is that they are bound lexically to the scope in which they are defined. From 'Arrow functions' on MDN:

An arrow function expression has a shorter syntax compared to function expressions and lexically binds the this value. Arrow functions are always anonymous.

This is particularly pertinent in your example considering that it is taken from a application. As as pointed out by @naomik, in React you often access a component's member functions using this. For example:

Unbound                     Explicitly bound            Implicitly bound 
------------------------------------------------------------------------------
function (field) {         |  function (field) {       |  field => e => {
  return function (e) {    |    return function (e) {  |    
      this.setState(...)   |      this.setState(...)   |    this.setState(...)
  }                        |    }.bind(this)           |    
}                          |  }.bind(this)             |  }