What is the pourpose of the last '+'(plus) sign?
I'm assuming you understand what the post- and pre-increments are doing here. As for the last +: you're using the unary + operator (JLS §15.15.3), just as in
int a = +1;
int b = 1 + +1;
And why Java allow this as a valid statement?
That's not really a meaningful question. The correct answer to it is "because the JLS says it's allowed". As for why that's the case, we can only speculate, but it makes sense to incorporate a unary plus for the sake of symmetry with unary minus. Unary plus can also be used for numeric promotion; from the link above:
Unary numeric promotion (§5.6.1) is performed on the operand. The type of the unary plus expression is the promoted type of the operand. The result of the unary plus expression is not a variable, but a value, even if the result of the operand expression is a variable.
At run time, the value of the unary plus expression is the promoted value of the operand.