Having an Overwhelming aura means two things, both related to detect magic.
First, it means that the item detects as an "Overwhelming" power source of magic. This just means that it involves a 10th level or higher spell, or a 21st or higher caster level. There is nothing in the description of Detect Magic that says that you take any kind of penalty from looking at an Overwhelming source of magic, so you don't. It's just another descriptive word to describe magical power, like "Faint" or "Strong".
Second, it means that the item leaves a source of Dim strength magic when it is destroyed for 1d6 days afterwards. This works like any other magical aura, it's just weaker than even the weakest spell.
There is a common misconception that looking at Overwhelming sources of magic is blinding or stunning, which comes from the description of the spell detect evil, which says:
If you are of good alignment, and the strongest evil aura's power is overwhelming (see below), and the HD or level of the aura's source is at least twice your character level, you are stunned for 1 round and the spell ends.
Unlike magic, if you detect a source of the opposing alignment that is both Overwhelming and twice your level, you get stunned. This only happens with alignments, though, not magic.