Cells in the root hairs of plants contain dissolved sugars and salts. Water surrounding the root moves into them to equalize the pressure. This is called osmosis. The increased water pressure in root hairs forces water upward, cell by cell through the roots and trunk to reach the leaves.
In addition to this, during the growing season, a tree passes tonnes of water into the atmosphere from its leaves through transpiration.
This creates a partial vacuum that is quickly filled by the water being pushed up from the roots. Water molecules stick together, and as water is lost during transpiration, this cohesion causes a chain reaction that is transmitted all the way down.