http://www.mynhltraderumors.com/2009/11/19/the-tagging-rule-facing-the-chicago-blackhawks/
Here's a modern day example. Essentially tagging prevents a team from signing players to deals that would put them over the cap THIS year even if that cap is expected to go up the following year.
For example let's use the Kings cap that GB posted a link to. The cap this year is at $69 million, while the Kings cap is at $68 million currently. They would not be allowed to sign someone for $2 million this offseason until they shedded $1 million from their current cap hit, or sign someone at $3 million without shedding $2 million, etc. etc. The cap moving up to $71 million next year is irrelevant.
Hope that helped.