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Wikipedia defines atom as

The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons.

and defines electron as:

The electron is a subatomic particle with a negative elementary electric charge. An electron has no known components or substructure; in other words, it is generally thought to be an elementary particle.

My confusion is:

Why is atom being called as basic unit of matter, when it consists of electrons, protons etc, which have masses. These particles electrons should be called as basic unit of matters, instead.?

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The particles such as electrons and protons (or electrons and quarks, depending on how deeply one gets; when you look carefully, even protons may be decomposed to smaller pieces) are called "elementary particles", not "units of matter".

The term "unit of matter" is meant to convey the information that a given chemical compound, a given material, is only composed of the same "units of matter". For example, water (a type of matter) is composed of water molecules and nothing else. The word "unit" would sound strange for electrons and protons because water is composed both of electrons and protons (and neutrons), so an electron isn't a unique "unit" of water. It is just one of the... elementary particles.

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You are right. Electrons and protons are basic units of matter. Its just historical confusion (electrons were discovered only in 20th century, while chemistry is very old), since atoms define basic chemical properties of matter its more convenient to call them basic units.

To sum up - in chemistry atoms and molecules are basic units of matter, in physics - electron, proton, neutron and so on.

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Both protons and neutrons have substructure and are made up of still more fundamental units. At the valence level each contains three quarks, but you should not discount the nucleon sea as quantum field theories dominate on this scale. – dmckee Aug 6 '12 at 20:41

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