With this Neopixel strip there are 60 RGB LEDs per meter, and you can control each LED individually! Yes, that's right, this is the digitally-addressable type of LED strip. You can set the color of each LED's red, green and blue component with 8-bit PWM precision (so 24-bit color per pixel). The LEDs are controlled by shift-registers that are chained up down the strip so you can shorten or lengthen the strip. Only 1 digital output pin are required to send data down. The PWM is built into each LED-chip so once you set the color you can stop talking to the strip and it will continue to PWM all the LEDs for you.
The strip is made of flexible PCB material, and comes with a weatherproof sheathing. You can cut this stuff pretty easily with wire cutters, there are cut-lines every 0.65"/1.7cm (1 LED each). Solder to the 0.1" copper pads and you're good to go. Of course, you can also connect strips together to make them longer, just watch how much current you need! You must use a 5V DC power supply to power these strips, do not use higher than 6V or you can destroy the entire strip.
These strips are sold by the meter! If you buy 5 meters at a time, you'll get full reels with two connectors. If you buy less than 4m, you'll get a single strip, but it will be a cut piece from a reel which may or may not have a connector on it.
WARNING: Please consult the Adafruit Guide to learn the correct method to power these strips. A 1000uF capacitor and a small 330ohm resistor may be required.
Adafruit's detailed NeoPixel Uberguide has everything you need to use NeoPixels in any shape and size. Including ready-to-go library & example code for the Arduino UNO/Duemilanove/Diecimila, Flora/Micro/Leonardo, Trinket/Gemma, Arduino Due & Arduino Mega/ADK (all versions)