Shruti texts are considered "Apurushaya" while Smriti texts are considered "Purusheya". So Vedas which are part of the Shruti Shastras are called Apurusheya while Puranas, which are part of Smriti Shahstra are called Purusheya.
"Purush" in Sanskrit means a man, so "Purusheya" means "of a man" while "Apurusheya" means "not of a man".
To truly understand what Apurusheya means we need to understand the term Shruti correctly. Shruti mentioned previously means "that which is heard". This means that the knowledge of the Vedas was revealed to our ancient Rishis and these rishis then carefully composed the Vedas to transfer this knowledge generation by generation. The point to focus here is “revealed”. A knowledge that is revealed is something that is discovered instead of being invented.
Moreover since Shruti is discovered and not invented, how can any person put his or her name to it? This knowledge cannot belong to one person it belongs to everyone. The knowledge is said to be revealed by God, because this knowledge was always there, it was just that we were not aware to it. This is the reason why authors of Shruti Shastras are unknown. Because if a name is added to this knowledge then it becomes subjective and absolute truth cannot be subjective.
The Vedas are not called Apurusheya because nobody wrote them. They are called Apurusheya because knowledge revealed in them is the ultimate truth and therefore it does not belong to a certain person but is universal.
"It is enjoyable to express the reality that Veda is the structure of consciousness; Veda itself is also the structuring dynamics of consciousness. Veda is the structuring dynamics of its own structure, that is why Apaurusheya - it is not created by anyone - it is created by itself. Veda is structured in consciousness, or Veda is structured intelligence structured by its own self-interacting dynamics."
Maharishi Mahesh Yogi: Maharishi Apaurusheya Bhashya – the discovery of the evolution of human life and all of creation, Maharishi explains the nature of the Shruti:1997, p. 164