Usually, increasing means you work two stitches in the same stitch, but since this one says to work three, then yeah -- single crochet three stitches in the same stitch.
However, that bit you posted doesn't say "inc 2," just "inc 1." So in round one, you'll have six single crochet stitches. In round two, you'll work two single crochets in each of the original six stitches, for a total of twelve. Round three, single crochet in the first stitch, then work two single crochets in the next stitch, and repeat that around, for a total of eighteen stitches in the round. For round four, work one single crochet in the first stitch, one in the second, and then two in the third. One, one, two, one, one, two, and so on. There'll be twenty-four stitches in the round.
What you're doing is adding six stitches in each round at regularly-spaced intervals. wink