Explanation

String one = "One";

if(userInput == one) 
{
  return true;
}
return false;

Assume userInput is a string input by the user (That is "One"). This will return false, while


if(userInput.equals(one))
{
  return true;
}
return false;


This will return true.

You can also do 

if(userInput.equalsIgnoreCase(one))
{
  return true;
}
return false;

will return true ignoring case.