+'a' resolves to NaN (“Not a Number”) because it coerces a string to a number, while the character a cannot be parsed as a number.
document.write(+'a');To lowercase it becomes banana.
Adding NaN to "ba" turns NaN into the string "NaN" due to type conversion, gives baNaN.
And then there is an a behind, giving baNaNa.
The space between + + is to make the first one string concatenation and the second one a unary plus (i.e. “positive”) operator.
You have the same result if you use 'ba'+(+'a')+'a', resolved as 'ba'+NaN+'a', which is equivalent to 'ba'+'NaN'+'a' due to type juggling.
document.write('ba'+(+'a')+'a');