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How do cell store energy and release energy using ATP?

Answer
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Hint: ATP is the currency of energy. This molecule is used by the cell for expending energy on a chemical reaction. For example, we are breaking the inorganic molecules to form organic molecules. ATP was discovered by Lohmann in $1929$. He isolated the first ATP molecule from the liver and muscles. ATP is synthesized by all types of organisms as they are important for extracting energy.

Complete answer:
We all need energy to do work. This energy is provided to us by food. When two bonds are broken, either energy is given to the molecule to break the bond or energy is released by the molecule.
This released energy is used by our body and cells to perform their activities.
ATP (Adenosine triphosphate) is a molecule which helps the cell to expend energy when it is needed during metabolic processes or any other processes.
ATP is an adenine molecule (nucleic acid) which is bounded to three- phosphate molecule and hence its name- Adenosine tri- phosphate.
This molecule is phosphorylated by enzymes during a process where energy is needed, the molecule loses one of its Phosphorus atoms and becomes Adenosine Di- phosphate (ADP).
ADP now travels to mitochondria where it gains a phosphate atom but this process requires energy.
This new bond carries energy within itself and the cell breaks down ATP back to ADP to extract the energy.
Hence, Mitochondria are called the powerhouse of the cell as it helps in processing ATP molecules. ATP is now transported to where it is needed and to the other cells. These cells, when they need energy, break ATP molecules into ADP molecules.
When phosphate bond breaks, it results in release of energy which is consumed in the process taking place inside the cell, for example, for the production of sucrose. In this way, the ATP helps in providing energy to the cell.

Note: ATP is synthesized in the cells with the help of an enzyme called “ATP synthase”. This enzyme helps convert Adenosine Di- phosphate (also known as adenine bisphosphate) into ATP. Energy can also be extracted by converting some more molecules like NADPH to NADP and the breakage of bond will provide energy equivalent to three ATPs. When $FADH2$ is converted to FAD, the breakage of bond releases energy equivalent to two ATPs.