Osmosis is essentially the diffusion of water through a cellular membrane. Osmosis moves down a concentration gradient- this means that water moves from an area of higher concentration (where there is more water) to an area of lower concentration (where there is less water). Osmosis will continue until there equal amounts of water on either side of the cellular membrane. This is the point of equilibrium.
One function of osmosis in plants is to create what is called turgor pressure. As the large vacuoles of a plant cell fill with water, they push the cell membrane against the cell wall. This gives the plant structure and rigidity. Without enough turgor pressure (from a lack of water, such as during a drought), the plant will wilt.
Such turgor pressure is also responsible to opening the guard cells that lie on either side of the stomata (small pores under the leaf). With enough turgor pressure (from osmosis), the guard cells open. Once open, carbon dioxide is able to enter the leaf. Carbon dioxide is imperative for photosynthesis. Photosynthesis is the process in which plant cells use their chlorophyll to capture sunlight energy in order to convert carbon dioxide and water into oxygen gas and glucose (a sugar). Plants then use the sugar as a source of energy.