You have asked about a very important, classic question in biology. It is important because the answer to your question explains much about life on Earth.

Photosynthetic organisms, like plants, use the energy that they "capture" from sunlight to make the fuel that they use to live. This fuel is a type of chemical energy, something we call ATP. The plant can convert harvested sunlight into this chemical energy (ATP). Then, they use the ATP to make a type of "stored fuel" - sugars. They make these sugars (carbohydrates) from carbon dioxide and water. When they use the ATP to drive the production of the sugars from the carbon dioxide and water, oxygen gets released.

More than 10 billion tons of carbons are "fixed" by plants on Earth every year - this means that carbon molecules are converted from being part of a simple gas (carbon dioxide) into more complex molecules (carbohydrates), making carbon available as food for non-photosynthesizers, like humans. They also produce oxygen at the same time. Take a look at a tree - most of the mass of that tree was made by this process of pulling the carbon out of the gas form and into the sugar form. Amazing!

Sunlight provides energy in the form of electromagnetic radiation. Sunlight is actually made up of photons, which are very small particles that carry electromagnetic force. In the first step of photosynthesis, the plants capture a photon and harness its energy in order to start photosynthesis. During photosynthesis, the plants take carbon dioxide (which is present throughout the air) and water (which is also in the air and dirt) and turn it into sugar, among other compounds. Plants also produce oxygen during photosynthesis. (This is a lucky process for us because we produce carbon dioxide and breathe in oxygen -- without plants, we'd be in a lot of trouble!)

Amazingly, some animals have been found that also do photosynthesis. I recently wrote an article on such an animal -- here is the link if you're interested (it also talks more about photosynthesis):

Photosynthesis takes place in two stages, the first of which captures the energy, and the second which makes sugars. The first one requires water, because the plant uses the hydrogen atoms in water to collect the energy. The second requires both: sugar contains carbon, oxygen, and hydrogen, of which the first two come from carbon dioxide and the last, comes from water. The excess oxygen is released as oxygen gas.