An idea separated from a complex object, or from other ideas which naturally accompany it; as the solidity of marble when contemplated apart from its color or figure. --Wikipedia
An abstract idea is an idea that can be interpreted in many different ways.
Some examples include:
Betrayal, Charity, Courage, Cowardice, Cruelty, Forgiveness, Truth, Love, Anger, Fear, Grief, Happiness, Jealously, Sympathy, Insanity, Knowldege, Wisdom, Right/Wrong, Duty, Fame, Justice, Liberty, Friendship, Greed, Innocence, Rules, Social Norm, and Religion.
Usually these abstract terms are difficult to define alone, but easier when in context. For example: What is Right? vs. What is the right answer to this math equation?
For most people it will be easier to answer the second question, because it is in context.
In OP's context, it seems the reference (along with theoretical arguments) is to concepts of philosophy.
Abstract ideas are concepts that need to be visualized, as they cannot be illustrated through concrete (real) examples. In a simple way, explaining the progression of logic in a (computer) program will be possible only if the reader can correctly visualize (imagine) it in his mind.