Energy
Energy is the ability to do work or cause change; it exists in forms such as kinetic, potential, thermal, and light and is measured in joules.
Definition
Energy is what makes things happen: the ability to move something, heat something, light something up, or make a sound. It is the capacity to do work or produce change, and it comes in many forms, including kinetic (motion), potential (stored by position or condition), thermal, chemical, electrical, light, sound, and nuclear. The SI unit is the joule (J), the work done by a $1\ \text{N}$ force over $1\ \text{m}$, and energy can be transferred and transformed but never created or destroyed. Formally, energy is a conserved scalar quantity associated with the state of a system; mechanical forms are kinetic energy $K = \tfrac{1}{2}mv^2$ and potential energy $U$, defined for conservative forces by $F = -dU/dx$, and the work-energy theorem $W_{\text{net}} = \Delta K$ links force to energy. Conservation of energy follows from time-translation symmetry (Noether's theorem), and in relativity mass itself is a form of energy, $E = mc^2$.
Example
The food you eat gives you energy to run, a battery stores energy to light a flashlight, and sunlight carries energy that warms your face. Lifting a $2\ \text{kg}$ book $1.5\ \text{m}$ onto a shelf takes $W = mgh = 2 \times 9.8 \times 1.5 = 29.4\ \text{J}$ of work, and the book then stores $29.4\ \text{J}$ of gravitational potential energy. A $0.5\ \text{kg}$ ball dropped from $10\ \text{m}$ starts with $U = 0.5 \times 9.8 \times 10 = 49\ \text{J}$, and just before impact all of it is kinetic: $\tfrac{1}{2}(0.5)v^2 = 49$, so $v = 14\ \text{m/s}$. No forces were needed, just bookkeeping.
Key Insight
Energy is never used up. When you ride a bike, the energy from your breakfast turns into motion and heat; it changes form but does not vanish. Every energy story ends with heat, because whatever form energy starts in, friction and other losses eventually spread it out as thermal energy that is hard to gather back up. Energy is best thought of as a bookkeeping tool rather than a substance. Its power comes from the fact that the total never changes, so a hard problem about forces often becomes an easy problem about before-and-after totals.