Here's what All the Words mean. Take a minute to read through so you have a handle on the basics.
Programmable lights with three wire connections: power, ground, and data. These are really common, and come in lots of different form factors so they're a great place to start.
The mini-computer that tells the LEDs what to do. The Circuit Playground Express is the microcontroller we're using in this guide.
Power & Ground
The two wire connections that make electricity flow. Power is almost always the red wire, or a +, or labeled VOUT, and Ground is almost always the black wire, or a -, or labeled G.
You can connect power and ground to either end of of your NeoPixel strip, or to the middle, or basically anywhere you'd like, but it's important to NOT get them mixed up. Hooking these two up backwards is the quickest way to fry your project.
The third wire connection, which tells the LEDs what color to be, how bright, etc. This wire (often white or yellow) hooks up to one of the pads on your microcontroller. Labeled IN or OUT on the pixel strips.
Data must flow from IN (at the microcontroller end) to OUT, or the strips won't light up. There's no danger of frying your project if you hook this up wrong, it simply won't work.
When you're shopping for NeoPixels, you'll find them in both RGB and RGBW varieties. If you're just starting out, I recommend sticking with RGB for now -- not all programming applications support RGBW since they're still pretty new (at the time of writing).
What's the difference? The W stands for white, and the RGBW lights have four LEDs inside each pixel: red, green, blue, and white, instead of just the 3 red, green, and blue LEDs inside RGB pixels. You'd want to use RGBW if you're trying for a specific white-light look (though RGBs will make white light as well).