First see dilution. Don't look at Delusion. Then understand why dilution is a bad thing for existing shareholders and why an investor might want an "anti-dilution" provision in a contract.
Consider a perspective on dilution from that of the eyes of an entrepreneur: The eventual goal in any company is to create wealth for shareholders. In the beginning, the founder owns all of the "wealth" or at least the shares in the company. Over time, that founder gives away pieces of the company in the form of shares to various flavors of investor who give him money in return for shares of his company. The challenge in high capital cost companies for the founder is the enemy of all capital backed companies: dilution.
A new tractor company requires several hundred million dollars to start. By the time he is done with 11 round of financing, the founder likely owns less than 2% of the company after having started with 100%. Conversely, a company built from software (computer code) often requires a very small amount of money. That is, Yahoo! required only a little over $1MM of total capital until it reached break even. It chose to take on more capital because it believed that the dilution was worth the incremental capital raised so that it could take advantage of market opportunities. eBay was about the same. The great fortunes of the internet era were made in part because the founders suffered so little dilution that at the end they had tens of billions of dollars of wealth via their large percentage ownership stakes in the companies they founded.
So what would be an ANTI-dilutive act? How about the company buying back its own shares?