What does 'Moonshots' mean?

Solution 1:

Moonshot is a long-standing popular name for the Apollo program which landed the first man on the moon.

Its relevance here is that the landing was achieved by a 'crash' program dedicating immense resources to solving seemingly insurmountable technical problems in a very short timespan. As the article points out:

Gates has always believed in using technology to tackle the world’s biggest and most complex of challenges.

Solution 2:

The disambiguation of moonshot is in and of itself fairly interesting and worthy of commentary here.

As StoneyB rightly points out, a moonshot is generally understood to mean the Apollo moon landing. And, the pouring of massive resources into accelerating a complex program on a minimal time frame. Here is an excellent video presentation on moonshot thinking.

The notion of shooting the moon has a longer history than the Apollo Mission, however.

Jules Verne's 1865 classic From the Earth to the Moon features a giant space cannon by which 3 people are launched in a capsule to the moon.

What is most interesting about this concept is that like many of Verne's predictions of the future, it was eerily accurate. His calculations on escape velocity were close to accurate, but it turns out a true moonshot would require a muzzle length that would make it dangerous and impractical. This book would serve as a major inspiration for Gerald Bull, the lead engineer on Project HARP, which although ultimately unsuccessful was an attempt at cannon-based-non-rocket orbital entry methods.

In the card game, Hearts, a player may shoot the moon. In this risky maneuver, the player trying to shoot the moon attempts to play all 26 points in the game. If they successfully pull off the maneuver, they either subtract 26 points from their own total, or add 26 points to the other players while their score remains the same.

So, while moonshot is commonly understood to mean the 1961-1972 Apollo program, the phrase shoot the moon is frequently used to mean any complicated, risky maneuver with high minded ideals behind it.

Solution 3:

Headline writers jobs are severely constrained, and they don't have many outlets to express themselves in their jobs. This is just a playful pun. It juxtaposes the serious need for modern methods in health and sanitization with the imagery of "mooning".

As one twitter commenter says: