IncR is the abbreviation used for knitting into the stitch below in a way that makes your increase lean to the right. The incRp is a variation where you purl instead of knit. The mirror stitch of this is the incL and incLp.
incR – increase right
incRp – increase right purl
How to incR
This increase cannot be made in the first stitch in a row. It will undo that stitch from the previous row. It can be worked into a last stitch.
Use the right needle to pick up the top of the stitch below the first stitch on the left needle. Lift it onto the left needle and knit as a stitch. Count increase.
How to incRp
Use the right needle to pick up the top of the stitch below the first stitch on the left needle. Lift it onto the left needle and purl as a stitch. Count increase.
I usually work both of these increases without lifting the top of the stitch onto my left needle. This takes a little practice, but feels more efficient, and once perfected, puts less strain on the stitch while working the increase.
How to work an inc2 (also inc3)
Knit into top of stitch below first stitch on left needle then knit first stitch on left needle (see IncR) and then knit into the top of the stitch in the row below the stitch from the left needle just knitted (see incL). This increases 2 stitches from one stitch. Count 3 stitches.
Historical note: Patterns published before 2011 by Y2Knit have the incL counting as 1 stitch, but the incR was counted as 2 stitches because I included the increase and the stitch worked after it from the left needle as a single instruction. The difference from how I counted the incL caused a lot of questions (and consternation), so I discontinued counting the two decreases differently. When a pattern is updated (patterns downloadable to date have been changed), I change to the current method of only counting the increase and make all resulting changes.
See also: incL