so
$grades{$student} .= $grade . " "; is more like

$grades

No. It is this:

$grades{$student} = "$grades{$student}$grade ";
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The value of $grade, followed by a space (" "), is appended to any existing value of $grades{$student}. The . operator does texual concatination, whereas += is numeric, and will add the right-hand-side to the left. For example:

$x = 3;
$y = 4;
$x .= $y;  # gives 34
$x += $y;  # gives 7
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