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Some applications simulate a virtual USB or CD Rom drive as if a USB drive is attached to the computer.

Is there any configuration or application that provides a virtual USB drive, not for the the operating system itself, but for other equipments which accept USB drive, through a USB port.

So I'll have a virtual hard disk (e.g. a *.vdi file) in the computer, which is connected, through a USB socket, as a USB drive to some other equipment (e.g. a cell phone or a laptop).

You would need to add a USB Device/Peripheral controller to the computer, as opposed to the USB Host Controller they tend to come with.

Something like this: https://www.maximintegrated.com/en/products/interface/controllers-expanders/MAX3420E.html

Unfortunately, you'd have to find a way to wire it onto your motherboard. Technically, it can be done. Practically, you'd have to redesign the motherboard to include it. You might be lucky enough to find an SPI or I2C bus exposed somewhere on your motherboard to allow you to add it, but they're usually wired directly into whatever they're being used for unless you're using a dev board or single-board computer with exposed GPIO and other ports such as a Raspberry Pi.

The other option would be a USB On-the-Go Controller. Motherboards designed for embedded and portable devices tend to have a USB OTG (On-the-go) contoller, which can function as either a Host or Device controller. For example, the aforementioned Raspberry Pi has an On-the-Go Controller, but on all models except the Pi Zero that gets rewired to a host port or an onboard USB hub denying the use of USB device functionality. The BeagleBone Black has an OTG port.

That's not all though - once you've got the hardware, you'd also need the software. Linux has some useful kernel USB Gadget drivers ("USB gadget" is another term for USB peripheral/device) such as g_serial and g_ethernet that allow you to plug your device into another computer and be visible as a serial or ethernet-over-USB device (there are others for exposing a device as mass storage, which allow you to use a file as a block device and expose the computer as a mass storage gadget). The BeagleBone Black tends to come with this enabled by default, so you can simply plug it into your PC over USB and see it as a networked device - and I believe it also appears as a mass storage device by using a composite driver (which allows it to appear as multiple USB device types over a single connection.) The Pi Zero can use these, but does not by default. For Windows or other OSes, you'd probably have to write that device driver yourself.

So, theoretically, you can do it. You can tear down your desktop PC, try and find an unused compatible bus on the motherboard somewhere (most likely some unused pins on a controller IC), or a way to extend an internal I2C or SPI bus, or something you can tear out and replace, and solder a USB OTG or device controller chip onto it. Then you can install Linux and use a gadget driver, or write your own for another OS. Practically, unless you're a top-notch electronics engineer, you're not going to be able to do it. At least, not until someone comes out with that elusive adapter with a device or OTG port on it that plugs into a USB port (theoretically, that could be done with a microcontroller such an Arduino wired to a pair of USB device controller ICs), and writes the drivers to run it.

USB is dissymmetric: one side is a host, the other side is a peripheral device. You can't make a peripheral device act as a host or vice versa. It is possible for a USB port to be able to act as either side; this is called USB on-the-go and is present on some mobile phones and tablets. The ports are physically device-type ports, not host-type ports. I've never seen a PC with a device port. This requires electronics on the controller, it isn't enough to make a cable that fits on both ends.

So no, you won't be able to make a PC into a USB device.

If you want to use a computer as a USB storage device, you can use a mobile phone or tablet with a USB connection instead of using a PC.

You can consider using one of special "USB-USB bridged cables", sometimes called "USB networking cables". Like one mentioned in these articles:

• 
  Connecting Two PCs using USB-USB Cable,


• 
  Connecting two computers with a USB cable,


• 
  How to Link Two Computers Using a USB Cable.

They allow you to transfer files between two PCs. I've been using these kind of cables over ten years ago (in times of Windows XP) and in that times all such cables available to the market required a special driver and software. They let you transfer files only through special file commander, that shiped along with cable drivers on a installation disk and therefore did not allow one PC to act to another as pure USB external device.

I'm not sure, if anything has changed since then and if new solutions allow you only to transfer files using special software and -- if you can force one PC to act as an external device to another PC.

As explained in the answer by by Matt Thomson, it is not properly possible to make a physical USB port of a PC computer act as a USB slave device, as the USB slave controller is missing.

That means if we have an adapter board that can provide slave-mode USB (such as the Raspberry Pi Zero), we have to connect it to your host PC by a different channel, such as wired Ethernet. I have two different proposals what protocol you could run over that Ethernet connection:

(1) Expose the USB port over IP network.

Use software to expose the USB slave-mode port of the Raspberry Pi Zero as a virtual USB device to your PC. The USB/IP project provides this, by means of a driver that can transport USB over IP networks. Here is an example of using USB/IP to provide a simulated USB device to a computer – which would be your PC here.

What I don't know in this proposed solution is if the USB/IP software is already able to expose a USB slave port over IP network, or only a USB host port as normal.

But even if that works, you still have to set up or adapt device drivers on your PC in such a way that they (1) accept the incoming USB/IP connection as a USB connection, (2) provide USB slave-mode rather than USB host-mode, (3) simulate a USB mass storage device by serving the data from the assigned location (your .vdi file).

Overall, that's a complex way of doing it.

(2) Expose the file over IP network.

This is a much simpler way for how to utilize the Ethernet connection to the Raspberry Pi Zero: on the Raspberry Pi Zero, mount the data stored on your PC via a network file system. These files then appear logically as part of the Pi Zero's file system, and you can serve them with the Linux USB gadget driver to make the Raspberry Pi look like a USB mass storage device to connected devices.