For the record, this post has absolutely nothing to do with Anthony Weiner - get your mind out of the gutter!
A naked put is when you short-sell a put option without a short-stock position to cover the put position. It's a neutral-bullish trade that makes money on time-decay or upward price movement. I actually prefer to call these cash-covered puts, because if the underlying's price moves down you are going to be paying cash for the shares at expiration, albeit with a better basis than buying the shares here-now. Usually you do this because the stock is something you are ok with owning the shares of anyway.
A nearly-naked put is a bull-put vertical for which the long option is purchased way out-of-the money, maybe 3 or 4 strikes below the short-put. This WOTM long-put is not really meaningful for stopping your losses if the underlying sells-off but it does have the effect of conserving buying power. In a non-margin account, such as an IRA, you will be required to allocate 100% of the value of the shares to a cash-covered put trade. With the purchase of a the WOTM option, the buying power allocated to the trade is controlled by the difference of the strike prices (x 100 x no. contracts.) It is not hard to engineer a nearly-naked put trade in an IRA to achieve the same buying power allocation as a margin-covered put.
Now might be a good time to engage in these put-premium selling techniques. This is because sell-offs tend to push up the price of puts as investors seek protection on their long stock positions. So if you believe in buying support levels then selling the puts does the same thing but with time on your side. Going nearly-naked is the small-dog way of doing this.