Chemical Bond
A chemical bond is the attraction that holds atoms together in a molecule or compound, formed by transferring or sharing valence electrons.
Definition
A chemical bond is what holds two atoms together, and atoms bond by giving away, taking, or sharing their outer electrons. It is a strong attractive force formed when atoms transfer or share valence electrons to reach a stable outer shell: ionic bonds form between metals and nonmetals by electron transfer, covalent bonds form between nonmetals by electron sharing, and metallic bonds hold metal atoms together; breaking bonds absorbs energy and forming bonds releases it. Physically, a bond is a net attractive interaction that lowers the total energy of the system below that of the separated atoms, and bond energy is the enthalpy required to break one mole of the bond in the gas phase. Bond type is a continuum set by the electronegativity difference between atoms, with near zero giving nonpolar covalent, a moderate difference giving polar covalent, and a large difference (roughly above $1.7$ to $2.0$) giving predominantly ionic character, and shorter bonds with higher bond orders are stronger.
Example
In a water molecule, each hydrogen atom is bonded to the oxygen atom, and those two bonds are what make it water instead of loose hydrogen and oxygen. Sodium and chlorine form an ionic bond in $NaCl$ when sodium gives an electron to chlorine, two hydrogen atoms form a covalent bond in $H_2$ by sharing their electrons, and copper atoms in a wire share a common pool of electrons in metallic bonding. The $H$-$H$ bond energy is $436\text{ kJ/mol}$, $O$=$O$ is $498\text{ kJ/mol}$, and $O$-$H$ is $463\text{ kJ/mol}$, so for $2H_2 + O_2 \rightarrow 2H_2O$, breaking $2(436) + 498 = 1370\text{ kJ}$ and forming $4(463) = 1852\text{ kJ}$ gives an estimated $\Delta H \approx -482\text{ kJ}$, close to the measured $-484\text{ kJ}$.
Key Insight
Bonds are not tiny sticks; they are electrical attractions between positive nuclei and negative electrons. A chemical reaction is just bonds breaking and new bonds forming, and whether the reaction gives off heat depends on whether the new bonds are stronger than the old ones. The "ionic versus covalent" division is a teaching convenience, since even $NaCl$ has a little covalent character and even the $H$-$F$ bond is strongly polar, so electronegativity difference, not a label, tells you where a bond really sits.