Step 1: Concept
The octet rule states that atoms are stable when they have eight electrons in their valence shell.
Step 2: Meaning
Molecules with fewer than 8 electrons around the central atom are called electron-deficient molecules.
Step 3: Analysis
In $H_{2}O, PCl_{3},$ and $NH_{3}$, the central atoms ($O, P, N$) have 8 valence electrons. In $BF_{3}$, Boron has only 3 valence electrons and forms 3 bonds, resulting in only 6 electrons.
Step 4: Conclusion
Boron in $BF_{3}$ is an exception to the octet rule as it remains electron-deficient.
Final Answer: (C)