"A common feature of all such forms of inanimate and animate objects was the sense of awe or fear that they evoked " - means that early people used to worship both inanimate objects (like winds, fire, sea, etc.) and some living plants and animals (animate objects). The common thing among all these objects was that they could generate a feeling of either fear or surprise within the living organisms. 

"Societies which indulged in anthropocentric view of biology could register limited progress in biological knowledge " means - if people within societies classified organisms only on the basis of their signficance on human life, then there would not have been significant progress in the scientific approach towards the life-forms. For example, if people classified plants as vegetable, oil plants or timber-yielding plants, etc., they might have put sunflower and mustard plants under the group "oil-yielding plants" and not under families Asteraceae and Brassicaceae.

"Systematic and monumental description of life forms" - means describing life forms in an orderly manner such that their unique characters can be retained in the memory.

"Recognition of sharing of similarities among living organisms both horizontally and vertically "-  means to identify and record similarities between members of same group (horizontally) and between members of different groups (vertically down the lineage of evolution)

"Molecular traffic inside a cell" - refers to the various biomolecules present within a cell. These biomolecules move within the cells from one cell organelle to the other (representing "molecular traffic").