What is Molecular Gastronomy?
First of all, the term "molecular gastronomy" is almost universally derided by those who practice it and "Modernist cuisine" seems to have become the accepted nomenclature. The book Modernist Cuisine has what I regard as an excellent introduction to the movement and drawing the analogy with other Modernist movements in other artforms. The Modernist movement was about rejecting the lineage of everything that had come before and re-examining basic questions such  as "what is perception". Similarly, we can trace a direct lineage from Escoffier to Nouvelle Cuisine and Modernist cuisine seeks to break that lineage.

The best way I've come up with to describe the Modernist philosophy is "the use of technology to gain direct, precise control over temperature, humidity, pressure and texture". 

When you're poaching fish in a simmering stock, you want to bring the fish up to 45C by putting it in 80C stock that's heated by a 600C flame. You control point in this scenario is the knob of the stove which is the second derivative of the temperature of this fish. What's more, your feedback loop is entirely perceptual and based on human sensing and control. Modernist cuisine starts with the goal of bringing a fish up to 45C and determines the optimal way of accomplishing that goal which is sous vide. With Sous Vide, you are directly controlling the temperature of the fish and you're doing it precisely because you replace humans with automated feedback loops.

Another example might be reducing a sauce. In this case, you manipulate the vapor pressure of the liquid through the indirect application of heat. What you really want is to drive water off but you end up causing many inadvertent changes as well. With Modernist cuisine, you use a rotovap to control pressure directly and vacuum evaporate liquids without heating. 

Same with using a roux or cornstarch to thicken a gravy. Instead of indirectly controlling the texture of a sauce by picking from one of the dozen common, natural thickeners, Modernist cuisine starts from asking exactly what textural qualities you want from a sauce and then figuring out the right combination of starches, hydrocolloids and proteins that accomplish that task.

Modernist cuisine may seem complicated on the surface because so much of it is new and unfamiliar but I find it actually to be radically more simple than traditional cooking once you understand this ethos. Rather than a hodgepodge of tradition built up over millennia, Modernist cooking is simply about starting first from your desired goals of flavor, temperature, pressure &amp; texture and then figuring out the appropriate use of technology to accomplish that goal.