As I learnt so far is that Arduino UNO board has a socket for power input. The available power input range is between 7V - 20V, but the optimal usage range is 7V-12V.
Here I am wondering:
---> if there is a USB port for power supply, why do we need a power input socket?
---> Or there is a battery on-board to charge?
The Arduino Uno has no on-board battery. The dc barrel jack is provided to give you more options to power the Uno, which is handy for stand-alone applications (without USB-connection to a computer) and/or battery powered applications. It can also supply more current than the USB-connection, which can be necessary when using shields.
The current taken from the usb port is limited to 500 mA by by an auto resettable fuse on the Uno (the voltage is not regulated by the Uno). This is the same amount of current as the USB 2.0 standard specifies that a standard down stream port (computer USB port) should be capable to deliver (for USB 3.0 this is 900 mA).
The power taken from the barrel jack is regulated to 5 V by a voltage regulator, the NCP1117ST50T3G. To work properly, this regulator needs a voltage difference (dV) between input and output of 1.2 V (depending on output current and ambient temperature). This means that the minimum voltage on the barrel jack is 6.2 V.
The regulator has an internal thermal limiting circuit that limits the junction temperature to ca. 175°C. This determines the maximum power dissipation (= output current times dV) the regulator can handle at a given ambient temperature. The maximum allowable power dissipation also depends on the size of the copper pad under the cooling tab of the regulator. As I don't know this size it is difficult to calculate de maximum power dissipation precisely, but my guess is that at 25°C and 6.2 V a power dissipation of 1 Watt should be possible. This gives a maximum output current of 1/(6.2-5.0)=0.833A=833 mA. Of course, at higher input voltages the maximum output current is lower. For example at 12 V: 1/(12.0-5.0)=0.143A=143mA.
Many projects (robots, drones, 3D printers, light control, art) made with Arduino have actuators (relays, motors), lights and displays which require a 9 or 12 V power supply. To use this power supply for the Arduino too, you need a voltage regulator which converts the voltage level and filters the noise and fluctuations created for example by that actuators.
