I understand why var takes that name - it is variable, const - it is a constant, but what is the meaning behind the name for let, which scopes to the current block? Let it be?

Let is a mathematical statement that was adopted by early programming languages like Scheme and Basic. Variables are considered low level entities not suitable for higher levels of abstraction, thus the desire of many language designers to introduce similar but more powerful concepts like in Clojure, F#, Scala, where let might mean a value, or a variable that can be assigned, but not changed, which in turn lets the compiler catch more programming errors and optimize code better.

JavaScript has had var from the beginning, so they just needed another keyword, and just borrowed from dozens of other languages that use let already as a traditional keyword as close to var as possible, although in JavaScript let creates block scope local variable instead.

The most likely possibility is that it was the most idiomatic choice. Not only is it easy to speak, but rather intuitive to understand. Some could argue, even more so than var.

But I reckon there's a little more history to this.

From Wikipedia:

Dana Scott's LCF language was a stage in the evolution of lambda calculus into modern functional languages. This language introduced the let expression, which has appeared in most functional languages since that time. State-full imperative languages such as ALGOL and Pascal essentially implement a let expression, to implement restricted scope of functions, in block structures.

I would like to believe this was an inspiration too, for the let in Javascript.

I guess it follows mathematical tradition. In mathematics, it is often said "let x be arbitrary real number" or like that.

It does exactly what the var does with a scope difference. Now it can not take the name var since that is already taken.

So it looks that it has taken the next best name which has a semantic in an interesting English language construct.

let myPet = 'dog';

In English it says "Let my pet be a dog"

Adding to exebook's response, the mathematics usage of the keyword let also encapsulates well the scoping implications of let when used in Javascript/ES6. Specifically, just as the following ES6 code is not aware of the assignment in braces of toPrint when it prints out the value of 'Hello World',

let toPrint = 'Hello World.';
{
    let toPrint = 'Goodbye World.';
}
console.log(toPrint); // Prints 'Hello World'

let as used in formalized mathematics (especially the writing of proofs) indicates that the current instance of a variable exists only for the scope of that logical idea. In the following example, x immediately gains a new identity upon entering the new idea (usually these are concepts necessary to prove the main idea) and reverts immediately to the old x upon the conclusion of the sub-proof. Of course, just as in coding, this is considered somewhat confusing and so is usually avoided by choosing a different name for the other variable.

Let x be so and so...

&e;&n;&s;&p; Proof stuff

&e;&n;&s;&p;New Idea { Let x be something else ... prove something } Conclude New Idea

&e;&n;&s;&p;Prove main idea with old x

Let uses a more immediate block level limited scope whereas var is function scope or global scope typically.

It seems let was chosen most likely because it is found in so many other languages to define variables, such as BASIC, and many others.

I think JavaScript's indebtedness to Scheme is obvious here. Scheme not only has let, but has let*, let*-values, let-syntax, and let-values. (See, The Scheme Programming Language, 4th Ed.).

((The choice adds further credence to the notion that JavaScript is Lispy, but--before we get carried away--not homoiconic.))))

It could also mean something like "Lexical Environment Type or Tied".. It bothers me that it would simply be "let this be that". And let rec wouldn't make sense in lambda calculus.