It is a decrease that reduces from 3 stitches down to 1.
The k3tog creates a decrease that slants to the right.
When you do a k3tog, you need the third stitch to stay on top, meaning it needs to remain visible when you work it.
Let’s create a k3tog. Assume each of the pegs below have a stitch/loop on them.
Step 1: Move loop from peg 2 over to peg 3.
Step 2: Move loop from peg 1 over to peg 3.
Peg 3 has three loops on it, loop from peg 3 (at the very bottom), loop from peg 2, and loop from peg 1 (at the very top, near the cap of the peg).
Step 3: Knit the stitch, treat all three loops on peg 3 as one loop.
The p3tog is exactly like the k3tog, except instead of KNITTING at Step 3, you would PURL.