What happens on a microscopic or molecular level when meat "melts in your mouth"?

I don't know about bacon literally melting in one's mouth. I doubt that is possible. However, the term "melts in your mouth," when referring to meat, is usually used to describe an ultra tender preparation.

The sensation probably is mostly centered on how we perceive fat and collagen that were broken down during the cooking process. Collagen and fat actually do melt, and proper cooking of proteins known to "melt in your mouth" keeps much of these melted elements within the final product. Alternately, when you eat a "dry" piece of meat, it is likely overcooked, and fat and collagen have drained from your final product.

Fats and collagen melt at different temperatures, and depending on the preparation, need different cooking times to provide the ideal eating experience. Often, these items are cooked "low and slow". For example, say, a pork butt cooked at 190F (88C) for 12 to 18 hours, or a properly cooked stew. Collagen melts as low as 160F (71C). Fats melt in the 130F to 140F (54C to 60C) range.

No preparation of meat, that I am aware of, literally turns entirely to liquid in one's mouth.

As an aside, this creates an issue for people who use sous vide/low temperature cooking, as sometimes cooking temperatures are below those needed to melt fats and collagen. In that situation dramatically lengthening the cooking time can be helpful, if one wants to impact the texture of the final product.

It is very difficult to name some kind of chemical answer for your question, since the phrase is not a literal description of what is happening. Its usage is a combination of intentional metaphor and a misattribution of real perceptional phenomena.

First, let's consider the rare case of where the phrase is indeed a literal description. You can let a bite of some foods melt in your mouth - say ice cream, chocolate, or pure butter. Except for the intentionally chilled ice cream, these foods tend to be made up mostly out of fat, which is solid at room temperature but melts at body temperature. But: nobody exclaims "my sister's chocolates are so good, they melt in your mouth!"

Instead, the phrase is meant for foods which typically require some active chewing, but have been prepared in a way that the perception reminds the eater of food which simply melts in the mouth without chewing. I have commonly heard it applied to meat, or to sweet items made with dough, such as strudel or brioche, in exceptional cases also to vegetables.

The physical phenomena which create the association with a true melting item seem to be several:

• when the food offers little resistance to the teeth during chewing (tender/not tough)
• when the food's volume goes down rapidly, with very little chewing, the solid bite "disappears" while in the mouth. This has the same physical basis as the point above, but is separate on the level of perception.
• when the food covers the mouth in a liquid that has a taste and texture similar to melting fat. This "juice" is usually rich in actual fat, but for some cuts of meat, the primary texture driver is melted collagen (melted in during cooking, not in the mouth).

Obviously, this is the easiest to achieve with foods/recipes which do have enough fat content that some real fat melting happens, such as the bacon you mentioned. But in addition, they have to be selected and prepared in a way that the non-melting portion is tender and gives way under the teeth.