It is possible to use some USB hubs without a power supply, however, doing so may prevent the USB hub or certain high-power USB peripherals from operating.  It is always recommended to use an included power supply with a USB hub when possible.
When a power adapter is not used on a hub that comes with a power adapter, power is drawn from the USB port on the computer and then divided between the ports on the hub. This reduces the power delivery to individual ports and high-powered USB peripherals, such as external hard drives, may not start.
On USB hubs that can use a power adapter, more power can be supplied to USB ports than what is possible with a single USB port.
If your USB peripherals require power adapters, they probably do not require power from the USB port and can be used on a USB hub without a power adapter. With USB peripherals that use power adapters, the USB ports on the hub are only used for data transfer and do not draw power from the hub.
USB peripherals that require low power (for example, keyboards and mice) can be used on hubs without a power adapter, in conjunction with other low-power USB peripherals. In this case, power is drawn from the computer's USB port, as described above.