Scientific names are used to identify and classify different species of organisms. They are based on the binomial nomenclature system, which was developed by Carl Linnaeus in the 18th century. According to this system, every species is given a unique two-part name consisting of a genus name and a species name.

In the case of a lion, the correct scientific name is Panthera leo. Let's break down this name and understand its components:

1. Genus Name: Panthera
- The genus name is always capitalized and italicized.
- It represents a group of closely related species that share common characteristics.
- In this case, the genus name is Panthera, which includes other big cats such as tigers, leopards, and jaguars.

2. Species Name: leo
- The species name is always written in lowercase and italicized.
- It represents a specific species within the genus.
- In this case, the species name is leo, which refers to the specific species of lion.

Combining the genus name (Panthera) and the species name (leo) gives us the complete scientific name for a lion, which is Panthera leo.

Now let's look at the other options and understand why they are incorrect:

a) Mangifera indica: This is the scientific name for the mango tree, not a lion.
b) Solanum tuberosum: This is the scientific name for the potato plant, not a lion.
c) Panthera nigra: This is not a valid scientific name. The species name "nigra" is not used to classify lions.

Therefore, the correct representation of the scientific name for a lion is option 'D': Panthera leo.