Flax Seeds are seeds that occasionaly drop when you break long grass. They are beigeish in colour, look like normal seeds and are planted in much the same way. They are used for farming string, basically the agricultural version of spider farming.
You can plant them on tilled soil but be aware the soil must be hydrated or they won't plant. When planted they grow until they are one block high and then another block spawns above them that has little dark blue flowers at the top.
When the top part of the plant is broken it drops some string and some more Flax Seeds.
Farming Flax Plants is easy because, much like sugar cane, you can break the top part of the plant, leaving the bottom part intact, ready to be grown again.
Bonemeal does work on Flax Plants but there is a glitch in which if the flax plant is half grown (i.e., last growth before top flowers grows) then the bonemeal does not work. Using the bonemeal on new or growing Flax Plants automatically grows them all the way, including the flower block at the top.