Your Arduino has some lights that it can use to give you an idea of what it is up to.
These lights, called LEDs (pronounced Ell Eee Dee), are on just about every electronic device you own. Often times they're used to let you know if something is on and if there's an error. For example, here's a cable modem with multiple LEDs.
Each LED indicates the status of the modem. For example, on this device the one on the top is the POWER LED, its lit if there's good power. In the middle is the ONLINE LED, which lets you know if the modem was able to connect to the Internet. Below, there is the 2.4GHz and 5GHz LEDs, that blink when you upload or download data through the modem.
Likewise, the Arduino has four LEDs: L, RX, TX, and ON
On the UNO, three are in the middle and one is to the right
On different Arduino variants, the LEDs may be in a different location. Like on this Metro, they're all on the left in a row
The four LEDs include three 'automatic' LEDs and one 'user controllable' LED:
ON LED - this LED will shine green whenever the Arduino is powered. Always check this LED if your Arduino is not acting right, if its flickering or off then you should check your power supply
RX and TX LEDs - these are like the 'send' and 'receive' LEDs on your cable modem. They blink whenever information is sent from or to the Arduino through the USB connection
The TX LED lights up yellow whenever data is sent from the Arduino to the computer USB port
The RX LED lights up yellow whenever data is sent to the Arduino from the computer USB port
L LED - this is the one LED that you can control. The ON, RX and TX LEDs all light up automatically no matter what. The L LED, however, is connected to the Arduino main chip and you can turn it on or off when you start writing code.
For future reference, L is connected to Digital Pin #13