Root pressure is the idea that because the roots take in ions by active transport, water is absorbed by osmosis due do the change in water potential (the roots are more "salty" [DONT EVER USE THAT TERM IN AN EXAM] because of all the ions they've absorbed). This means that water is constantly being drawn in. This water moves with the ions (to keep a constant osmotic potential) and moves up the plants stalk to wherever the ions are going, once they are used up the water moves by osmosis to anywhere in the plant that has a low osmotic potential.
Evidence to support this is the fact that if you make a cut low in a plant stalk water comes out, but continues to come out (i.e. its not just a release of pressure, but something is actively pushing water up from the roots).
The water itself moves by cohesion because of hydrogen bonding which makes it stick to itself an means that it can form water columns (like when you draw water up in a straw). Because of this water can be "sucked up" a plant stalk.
A lot of water is also drawn by the transpiration stream (as mentioned above) which is where water evaporates from the stomata in the leaves, so water moves from the roots up to the leaves (a high osmotic potential to a low osmotic potential). This then means there is less water in roots, so water is drawn into the roots by osmosis.