**Explanation:**

**Electrolysis** is a process that uses an electric current to drive a non-spontaneous chemical reaction. It involves the decomposition of a compound into its constituent elements or ions.

In the case of electrolysis of aqueous NaCl (sodium chloride) solution, the compound dissociates into its constituent ions, Na+ and Cl-. The Na+ ions are attracted to the cathode (negative electrode), while the Cl- ions are attracted to the anode (positive electrode). The following reactions take place at the respective electrodes:

**1. Cathode (Negative Electrode):**
At the cathode, the water molecules (H2O) are reduced by gaining electrons from the cathode. This leads to the formation of hydrogen gas (H2) and hydroxide ions (OH-). The overall reaction is as follows:

2H2O + 2e- -> H2 + 2OH-

Therefore, hydrogen gas (H2) is produced at the cathode during the electrolysis of aqueous NaCl.

**2. Anode (Positive Electrode):**
At the anode, chloride ions (Cl-) are oxidized by losing electrons to the anode. This results in the formation of chlorine gas (Cl2) and releases electrons. The overall reaction can be represented as:

2Cl- -> Cl2 + 2e-

Therefore, chlorine gas (Cl2) is produced at the anode during the electrolysis of aqueous NaCl.

**3. Absence of O2 (Oxygen) Production:**
Although water (H2O) is present in the electrolyte, oxygen gas (O2) is not produced during the electrolysis of aqueous NaCl. This is because the reduction of water molecules (H2O) to produce oxygen gas (O2) requires a higher voltage compared to the reduction of water to produce hydrogen gas (H2). In the presence of chloride ions (Cl-), the reduction of water to produce hydrogen gas (H2) is favored due to its lower voltage requirement.

Hence, the production of hydrogen gas (H2) and chlorine gas (Cl2) takes precedence over the production of oxygen gas (O2) during the electrolysis of aqueous NaCl.