Amines are an important class of organic compounds that contain one or more nitrogen atoms bonded to hydrocarbon groups. They are derived from ammonia by replacement of one or more hydrogen atoms by alkyl or aryl groups.

The primary commercial use of amines includes the synthesis of various compounds. Let's evaluate the given options:

1. Development of explosives: While certain amines can be used in the production of explosives, it is not their primary commercial use. The use of amines in explosives is limited compared to their use in other industries.
2. Synthesis of medicines and fibres: This is the correct answer. Amines are widely used in the synthesis of pharmaceuticals. They serve as building blocks for a variety of drugs, including pain relievers, antibiotics, and antihistamines. Additionally, amines are used in the production of synthetic fibres, such as nylon and polyurethane.
3. Development of batteries: Amines are not commonly used in the development of batteries. The primary materials for batteries involve metals and electrolytes that facilitate the storage and release of energy.
4. Stem cell therapy: Amines are not directly used in stem cell therapy. This field primarily involves biological elements like cell cultures, growth factors, and scaffolds.

Based on the above analysis, the primary commercial use of amines is Synthesis of medicines and fibres, making this the correct answer.