The TX and RX leds are used when data is being transmitted through the USB port. Quoting from the description of the UNO:
The Arduino software includes a serial monitor which allows simple textual data to be sent to and from the Arduino board. The RX and TX LEDs on the board will flash when data is being transmitted via the USB-to-serial chip and USB connection to the computer (but not for serial communication on pins 0 and 1).
So, if you do Serial.print/Serial.println it should flash the TX light. If the host sends you data that you read with Serial.read, then the RX light should be lit.
The 4th led is the power light. It is on if the board has power.
If you want any other LEDs, you have to add them yourself. Be sure to use appropriate resistors on LEDs, or else you might burn out the LED or damage your UNO. Here is an example that shows how to wire up a LED:
http://arduino.cc/en/Tutorial/Fade.