esModuleInterop generates the helpers outlined in the docs. Looking at the generated code, we can see exactly what these do:

//ts 
import React from 'react'
//js 
var __importDefault = (this && this.__importDefault) || function (mod) {
    return (mod && mod.__esModule) ? mod : { "default": mod };
};
Object.defineProperty(exports, "__esModule", { value: true });
var react_1 = __importDefault(require("react"));

__importDefault: If the module is not an es module then what is returned by require becomes the default. This means that if you use default import on a commonjs module, the whole module is actually the default.

__importStar is best described in this PR:

TypeScript treats a namespace import (i.e. import * as foo from "foo") as equivalent to const foo = require("foo"). Things are simple here, but they don't work out if the primary object being imported is a primitive or a value with call/construct signatures. ECMAScript basically says a namespace record is a plain object.

Babel first requires in the module, and checks for a property named __esModule. If __esModule is set to true, then the behavior is the same as that of TypeScript, but otherwise, it synthesizes a namespace record where:

1. All properties are plucked off of the require'd module and made available as named imports.
2. The originally require'd module is made available as a default import.

So we get this:

// ts
import * as React from 'react'

// emitted js
var __importStar = (this && this.__importStar) || function (mod) {
    if (mod && mod.__esModule) return mod;
    var result = {};
    if (mod != null) for (var k in mod) if (Object.hasOwnProperty.call(mod, k)) result[k] = mod[k];
    result["default"] = mod;
    return result;
};
Object.defineProperty(exports, "__esModule", { value: true });
var React = __importStar(require("react"));

allowSyntheticDefaultImports is the companion to all of this, setting this to false will not change the emitted helpers (both of them will still look the same). But it will raise a typescript error if you are using default import for a commonjs module. So this import React from 'react' will raise the error Module '".../node_modules/@types/react/index"' has no default export. if allowSyntheticDefaultImports is false.

Problem statement

Problem occurs when we want to import CommonJS module into ES6 module codebase.

Before these flags we had to import CommonJS modules with star (* as something) import:

// node_modules/moment/index.js
exports = moment

// index.ts file in our app
import * as moment from 'moment'
moment(); // not compliant with es6 module spec

// transpiled js (simplified):
const moment = require("moment");
moment();

We can see that * was somehow equivalent to exports variable. It worked fine, but it wasn't compliant with es6 modules spec. In spec, the namespace record in star import (moment in our case) can be only a plain object, not callable (moment() is not allowed).

Solution

With flag esModuleInterop we can import CommonJS modules in compliance with es6 modules spec. Now our import code looks like this:

// index.ts file in our app
import moment from 'moment'
moment(); // compliant with es6 module spec

// transpiled js with esModuleInterop (simplified):
const moment = __importDefault(require('moment'));
moment.default();

It works and it's perfectly valid with es6 modules spec, because moment is not namespace from star import, it's default import.

But how does it work? As you can see, because we did a default import, we called the default property on a moment object. But we didn't declare a default property on the exports object in the moment library. The key is the __importDefault function. It assigns module (exports) to the default property for CommonJS modules:

var __importDefault = (this && this.__importDefault) || function (mod) {
    return (mod && mod.__esModule) ? mod : { "default": mod };
};

As you can see, we import es6 modules as they are, but CommonJS modules are wrapped into an object with the default key. This makes it possible to import defaults on CommonJS modules.

__importStar does the similar job - it returns untouched esModules, but translates CommonJS modules into modules with a default property:

// index.ts file in our app
import * as moment from 'moment'

// transpiled js with esModuleInterop (simplified):
const moment = __importStar(require("moment"));
// note that "moment" is now uncallable - ts will report error!

var __importStar = (this && this.__importStar) || function (mod) {
    if (mod && mod.__esModule) return mod;
    var result = {};
    if (mod != null) for (var k in mod) if (Object.hasOwnProperty.call(mod, k)) result[k] = mod[k];
    result["default"] = mod;
    return result;
};

Synthetic imports

And what about allowSyntheticDefaultImports - what is it for? Now the docs should be clear:

Allow default imports from modules with no default export. This does not affect code emit, just typechecking.

In moment typings we don't have specified default export, and we shouldn't have, because it's available only with flag esModuleInterop on. So allowSyntheticDefaultImports will not report an error if we want to import default from a third-party module which doesn't have a default export.

In my case (i am using a typescript project in VS2019 and react v16.13.xx) i had to replace

import React from 'react';

with

declare var require: any
var React = require('react');

and it worked