What does return *this; do, exactly?

[Tduck]

What happens when I return *this? Does it set the values of the object which used the ++ operator to themself + 1 or am I mistaking something?

rectangleType rectangleType::operator++(int u)
{
    this->length += 1;
    this->width += 1;
    return *this;
}

[keskiverto]

The this is a pointer to the object that the member function was called on.

For example:

rectangleType foo;
rectangleType bar;
foo++; // During the call   this == &foo
bar++; // During the call   this == &bar 

The * is normal pointer dereference.

Therefore,

bar = foo++;
// would do same as:
foo.length += 1;
foo.width += 1;
bar = foo;

Note that your post-increment operator does not return what they usually do:
https://en.cppreference.com/w/cpp/language/operator_incdec

bar = foo++;
// is usually equivalent to:
bar = foo;
foo.length += 1;
foo.width += 1;