What does "compare at" mean in ads?

Solution 1:

The first-posted answer explains the function of compare at in adertising, but does not explain why that particular construction came to serve that purpose (which seems to be a part of what puzzled the OP). The reason is that 'compare at $100', as used in advertising, is a conventional abbreviation for something like:

Compare this product, which we sell for $60, to the similar products that other sellers sell at $100, and you will see that they are essentially the same.

It is a part of this advertising strategy that the advertiser does not explicitly say that you will save $40 by buying the product from them, but leaves the appearance of encouraging you to make the comparison yourself and so reach that conclusion on your own.

Solution 2:

The compare at price is a price that the seller suggests this same item (or, as noted in comments, a comparable item) sells for elsewhere, or is the full retail price at some places.

It can be used to make the buyers believe that they are saving money, as there is no regulation in place to prevent inflating the compare at price to make the for sale price seem a better value.

See this article about a suit against a retail chain for misleading compare at prices.