The short answer is that when plants are doing cellular respiration, they produce carbon dioxide and water. When they are doing photosynthesis, they make oxygen and sugar.

So it’s not as strange as it seems. It’s just that they can use 2 different processes depending on the conditions.

Let’s look at the conditions. Like us, they need oxygen and sugar to do cellular respiration. Like us, they use the energy from breaking down the sugar to make ATP, a source of energy that all cells can use. Carbon dioxide and water are waste products. We get rid of them in different ways, of course. The reason you don’t weigh as much as all the groceries you eat is that you breathe out a lot of carbon dioxide and get rid of the water. We lose water in a lot of ways, including urination and sweating. Plants let it evaporate of their leaves. This also powers the movement of water up from the roots, so it’s important.

When they do photosynthesis, they need carbon dioxide, water, and light energy. They produce oxygen and sugar. The sugar can then be built up into things like starches, cellulose, and wood. Notice that light is a big deal. We talk a lot about plant cells doing photosynthesis, but lots of plant cells never do photosynthesis because they’re in parts of the plant that are not exposed to the light. They may be underground in roots or deep in the wood of a tree. They all need ATP, though. They get their sugar from leaf cells and do cellular respiration. The sugar travels to them via tubes that sort of act like our blood vessels. If I look out my window now, I see huge trees with no leaves. Their cells have to make it through the winter burning the sugar they’ve been making since last spring. So all the cells left in the tree are doing cellular respiration.

So here’s a puzzle for you. The sun still shines here (sometimes) in the winter, so why don’t trees like oaks, maples, and aspens just keep their leaves? Hint: I also see snow out my window.

Respiration in plants can occur in the dark or under sunlight. Respiration in the dark is commonly just called respiration; this process is very important to plants at night for energy production and only requires oxygen and sugars be supplied to the plant. The respiration that is possible under sunlight is called photorespiration; it is possible because of a protein called ribulose-1,5-bisphosphate carboxylase/oxygenase, abbreviated RuBisCO. RuBisCO is an enzyme that can catalyze reactions that use oxygen, ultimately causing carbon dioxide to be produced.

Photorespiration undercuts the results of photosynthesis because photorespiration takes away some of the carbon dioxide that photosynthesis is trying to use to produce energy for the plant. Since both processes can occur under sunlight, a plant can then produce oxygen (as a waste produce of photosynthesis) and carbon dioxide (as a waste product of photorespiration).

Keep in mind that in the dark, carbon dioxide is produced as a waste product of respiration as well, but in this case, respiration is not undercutting photosynthesis; it is simply a process by which plants use their storage of sugars to survive, and in the dark, plants do not produce oxygen.

Plants need energy during the night when there isn't enough light to photosynthesize. They get this energy the same way you do: by combining sugars with oxygen to produce carbon dioxide and water.

During the day, however, plants can get the energy they need from light, and use the excess energy to combine carbon dioxide with water to make sugars that they will burn during the night and to build up their bodies (plant bodies are mostly made out of polymers of sugar). This making sugar produces oxygen as a waste product.

Note that getting carbon dioxide out of the air also means losing water into the air. This means that some plants save up energy generated during the day to do the making of sugars at night. This usually happens in deserts.

Plants use food, just like we do. They make food by photosynthesis, but they use food by respiration to get energy. Here's a definition of Respiration:

BIOLOGY:
"a process in living organisms involving the production of energy, typically with the intake of oxygen and the release of carbon dioxide from the oxidation of complex organic substances">