Every Indifference Curve to the right represents Higher Level of Satisfaction than that of the Proceeding One:
Let us take two Indifference Curves IC1 and IC2 lying to the right of IC1. At the point P the consumer gets OM of oranges and ON of bananas. At the point Q though the number of bananas remains the same i.e., ON, yet the number of oranges increases from OM to OM1. The total satisfaction of the consumer is therefore bound to be greater at Q than at P.
Hence Q represents a more valued and preferred combination of oranges and bananas than P. As all the points on one Indifference Curve represents equal satisfaction, therefore every point on IC2 represents a combination, preferred to that represented by any point on IC. An Indifference Curve to the right represents a preferred position and therefore a consumer will always try to move on the indifference map as much to the right as possible.
Indifference Curves are Convex towards the Origin : Indifference curves are convex towards the origin because marginal rate of substitution continously decreases (because as the stock of one commodity decreases its marginal importance for the consumer will continously increases and as the stock of another commodity increases its marginal importance for the consumer will continously decreases, therefore he is ready to sacrifice lesser and lesser units of one commodity for the every extra unit of another commodity to maintain the same level of satisfaction).
As shown in the diagram when consumer increases one unit of X commodity he decreases Y commodity equal to PQ, whereas for next unit of X commodity he decreases Y commodity equal to QR. As we can see that PQ > QR, it represents that MRSxy is decreasing and due to that indifference curve will become convex towards the origin.