Indifference curves represent the various combinations of two goods that provide the same level of satisfaction or utility to an individual. These curves are typically downward sloping because as the quantity of one good increases, the individual is willing to give up less and less of the other good to maintain the same level of satisfaction.

The convexity of indifference curves is due to the concept of diminishing marginal rate of substitution (MRS). The MRS measures the rate at which an individual is willing to give up one good in exchange for another while maintaining the same level of satisfaction. It is the slope of the indifference curve at any given point.

Explanation:

1. Diminishing Marginal Rate of Substitution (MRS):
- The concept of MRS states that as an individual consumes more and more of one good, the marginal utility derived from each additional unit of that good decreases.
- This means that the individual is willing to give up less and less of the other good to obtain additional units of the first good.
- As a result, the slope of the indifference curve becomes flatter as we move along the curve from left to right.

2. Convexity of Indifference Curves:
- The convex shape of indifference curves reflects the diminishing MRS.
- When the MRS is diminishing, the slope of the indifference curve decreases as we move along the curve.
- This creates a convex shape because the curve becomes flatter towards the right and steeper towards the left.
- The convexity implies that the individual is willing to give up larger quantities of one good in exchange for small quantities of the other good at the beginning, but as they consume more of that good, they become less willing to give up as much of the other good.

Conclusion:
The correct answer is option 'A' - Declining marginal rate of substitution. The convexity of indifference curves is a result of the concept of diminishing marginal rate of substitution, which states that individuals are willing to give up less and less of one good to obtain additional units of the other good. This leads to a convex shape of indifference curves.