Unfortunately, whoever gave this 'advice' has no idea what they are talking about. Most modern laptops have dual-core processors, and without the battery plugged in they will only access a single core; meaning that you'd completely reduce your computer's power if you took the battery out. All that taking a battery out does is allow it to slowly drain.

Can you show any evidence (links or anything) for this claim?

<link>

Some maker of crappy laptops says so. Many engineers know that the processors underclock when the battery is out. Something about the capacitance of the system declining when the battery has been removed.

This doesn't say that the computer accesses only one processor core.

And as this Tom's Hardware piece explains, this behavior seems confined to Apple -- and it's no longer even applicable to Apple, because of course you can't remove Apple laptop batteries any longer. <link>

Just one more reason not to buy an Apple.