These provisions are commonly required by sophisticated investors to protect themselves in the case of a down round. A down round occurs when new money comes in at a lower pre-money valuation (or price per share) than the previous round post-money valuation. For example, if you close an angel round of $1M and agree upon a pre-money valuation of $4M, the post-money valuation will be $5M (pre-money valuation + money in). This means the investors will have purchased 20% of the company.
If you raise a subsequent round of $3M but can only negotiate a pre-money valuation of $4M the initial investors have essentially lost 20% ($5M-$4M = $1M, $1M/$5M = 20%) on their original investment.
Two types of anti-dilution are commonly used: Full Ratchet and Weighted Average.
If the original investors negotiated for a full ratchet anti-dilution then the common shareholders will have to dilute further in order to make the series A preferred shareholders whole. In the example above if the common shareholders held 1 million shares, this would be equivalent to giving up 200,000 shares to the series A preferred shareholders as a result of the additional dilution hit of the down round in order to maintain the original stake at the level they invested in the A round. This is a fairly simple explanation of the effects. For a more in depth analysis take a look here.
In the case of a weighted average anti-dillution, the series A investor is not made whole but are compensated. Their share price is reduced to the new price and the anti-dilution redistribution of shares is based upon the number of shares they currently have vs the total number shares in the company. Weighted Average Anti-dilution is, I believe, the most common form of anti-dilution provision and certainly the least onerous to founders.
In short: common shareholders are dilluted twice when a down round closes: first to make up for the down round dillution that occured to series A shareholders and second for the normal dillution that occurs when you take in new money.
Lesson: always involve your attorney when negotiating these terms and never accept full ratchet anti-dilution unless your back is completely against the wall. Obviously everyone hopes for subsequent rounds to increase the valuation of the company. Post bubble this has frequently not been the case. I believe the terms pendulum is currently swinging back in favor of the entrepeneur but it is always best to negotiate from a position of knowledge.
In the future I will cover liquidation preferences, reverse vesting, dividends, class voting rights and any other terms that have bitten me on the ass before. :)