k1b = knit 1 in the row below

k1b has two possible meanings: 

knit 1 in the row below: Insert needle through center of st 1 row below next st and knit, slipping st above off needle at same time. 

knit through back loop (though this is usually written kbl) in which case you knit into the back of the stitch instead of the front of the stitch. This gives a tighter stitch and is sometimes used for ribbing.