Fermentation allows glycolysis to continue when respiratory oxidation of NADH is unavailable or insufficient by transferring electrons from NADH to an organic molecule and thereby regenerating NAD$^+$.

Its essential purpose is redox balancing:

$$\boxed{\mathrm{NADH\rightarrow NAD^+}}.$$

Fermentation does not add a membrane electron-transport stage that produces large amounts of additional ATP. The ATP associated with fermentative glucose metabolism comes primarily from substrate-level phosphorylation in glycolysis.

Why NAD+ regeneration is necessary

Glycolysis contains an oxidation step that requires NAD$^+$. If the finite cellular NAD pool became entirely reduced to NADH, glycolysis would stop even if glucose and ADP remained available.

A fermentation reaction solves this by using a glycolytic product or derivative as the electron acceptor.

The logic is

glycolysis
NAD+ → NADH
   ↓
organic product accepts reducing equivalents
   ↓
NADH → NAD+
   ↓
regenerated NAD+ returns to glycolysis

Lactate fermentation

In lactate fermentation, pyruvate accepts reducing equivalents from NADH:

$$\mathrm{pyruvate+NADH+H^+\rightarrow lactate+NAD^+}.$$

No carbon dioxide is released in this conversion. The three carbons of pyruvate remain in lactate.

Combining this reaction with glycolysis gives a pathway that can maintain net ATP production without requiring a respiratory electron-transport chain.

Alcoholic fermentation

In many yeasts and microorganisms, pyruvate is first decarboxylated:

$$\mathrm{pyruvate\rightarrow acetaldehyde+CO_2},$$

then acetaldehyde accepts reducing equivalents:

$$\mathrm{acetaldehyde+NADH+H^+\rightarrow ethanol+NAD^+}.$$

Again, the redox function is to regenerate NAD$^+$.

Fermentation leaves substantial free energy in its products

Lactate and ethanol are still relatively reduced organic molecules. Fermentation therefore extracts much less of glucose's available oxidation free energy than complete aerobic oxidation.

This explains the low ATP yield: one glucose gives the glycolytic net of approximately

$$2\ \mathrm{ATP},$$

while NADH is recycled rather than used to build a membrane gradient for further ATP synthesis.

Fermentation is therefore a strategy for maintaining redox-carrier balance so substrate-level ATP production can continue.