What is index?
From my understanding index is a sign where it gives the direct meaning and it can be easily understand the purpose of the sign and the object in its direct point of views. We can recognize the object easily without having different meaning on it as the object is already exist and don’t need any advance interpretation for the object.
Examples:

The meaning of the directional signpost above represents school
crossing watch for pedestrian ahead.

The sign
shows the changes of climate
What is Symbol?
Symbol is a sign that does not show the direct meaning of the object. To get exact meaning or description of the object that we saw, we should learn deeper through the association. It does not show the real meaning, logic or connection between it. Any words are considered as symbol.
For an examples,

The color of red represents danger sign
What is Icons?
An icon is a sign where it represents the object in reality.it can be in form of photograph, illustrative or diagrammatic. Icon can gives into different meaning of what we had seen, it influenced by the cultural conventions.it is the simplest since the pattern physically resembles of what it seems to be.
For an example,

If this brings to mind a kind of fruit, it is acting as an icon