Intarsia is a knitting colorwork technique that involves knitting with blocks of color. They can be in any shape or design you like, but the key is that when you change colors you don't strand the colors you're not working with across the back as is done in stranded knitting (also known as Fair Isle).
Instead, each color of yarn is its own unit, with the strands being twisted together when you change colors to connect the pieces to each other.
It's an easy technique but it does require a bit of forethought because you need a different strand of each color to work with in your design. So, for example, this tutorial uses a two-color block of 20 stitches and 20 rows, with a 10-stitch, 10-row block of the second color in the center of the first.
To make that work you'll need one strand of your second color and two strands of the first -- one for each side of the square. For a small swatch like this you can just cut long strands a couple of yards each, but for a bigger project you might need actual balls of yarn to work with.
To set up your intarsia, knit any rows that don't include the color design. In this case I cast on 20 stitches and worked 5 rows, beginning and ending with a purl row.