In layman's terms, there are common shares, which have voting power. The SEC has regulations regarding how many shares can be held and under what conditions. They do this to protect public companies from those who hold a large number of shares who might use them in a manner to harm the company or other shareholders.
Warrants are an entitlement to shares when the required conditions are met to exercise them (payment, etc). They do not have voting rights, so they are exempt from the SEC rules that pertain to common shares.
Baker Brothers wanted a large stake in IDRA, and they could not have done it by buying common shares without being subject to the SEC rules that would REALLY complicate the situation, so they purchased warrants instead of common shares.
BB paid 3.99 per warrant, and they have to pay an additional .01 per warrant when they exercise them and convert to common shares. What this did was give the cash to the company as though they had sold the shares for the 4.00 offering price without BB actually owning the shares and having the voting power, which would have subjected them to the many SEC requirements that would have come from owning that many shares.
The verbiage about staying under 5% and 20% share ownership is all about avoiding the stringent SEC regulations they would be subject to if they were to own that many shares at one time.
It's all VERY GOOD for common shareholders.