Concept:
Ionization enthalpy is the minimum amount of energy required to remove the most loosely bound electron from an isolated gaseous atom.
Generally, ionization enthalpy increases across a period due to increasing effective nuclear charge. However, nitrogen and oxygen show an exception because of the stability associated with half-filled orbitals.
Nitrogen has the electronic configuration
\[
1s^22s^22p^3,
\]
which is a perfectly half-filled \(2p\) subshell. Half-filled and completely filled subshells possess extra stability due to symmetrical distribution of electrons and maximum exchange energy.
Oxygen has the electronic configuration
\[
1s^22s^22p^4,
\]
where one of the \(2p\) orbitals contains a pair of electrons. The repulsion between paired electrons makes it comparatively easier to remove one electron.
Step 1: Examine the assertion.
The first ionization enthalpy of nitrogen is greater than that of oxygen.
\[
IE_1(N)\gt IE_1(O)
\]
This statement is true because removing an electron from the stable half-filled configuration of nitrogen requires more energy.
Step 2: Examine the reason.
Nitrogen possesses the electronic configuration
\[
2p^3,
\]
which is a half-filled subshell.
Half-filled subshells are extra stable because of maximum exchange energy and symmetrical electron distribution.
Hence, the reason is also true.
Step 3: Determine whether the reason explains the assertion.
The higher stability of nitrogen due to its half-filled \(2p\) subshell directly explains why its first ionization enthalpy is higher than that of oxygen.
Therefore,
\[
\boxed{\text{Assertion is true, Reason is true, and Reason correctly explains the Assertion.}}
\]
Hence, the correct answer is
\[
\boxed{\textbf{Option (A)}}.
\]