Deeper meaning of 爲 (beyond one sentence definitions)
There are many meanings for 為.
「為」有非常多的意思。

The question is to ask the deeper meaning of 為 in 無為.
此問是問「無為」之「為」有何深義。

So，we should understand the meaning of 無為 first.
故需先了解「無為」之義。

The 無為 is mostly used in Taoism or Buddhism.
「無為」多為道家或佛家所用。

The following content is based on the Buddhist point of view.
以下所述乃基於佛教觀點。

The 無為 in the Dharma means 無因緣的造作.
佛法中的「無為」是指「無因緣的造作」。

It means not doing something for any reason, condition or circumstance.
意謂：非因任何理由、條件、環境而做某事。

Therefore, 為 refers to 造作, in particular 有因緣的造作.
是故「為」指「造作」，尤其是「有因緣的造作」。

That is to do something for some cause, condition or dependence.
也就是基於某些理由、條件、環境才做某事。

This 為 shows the phenomenon of creating, staying, changing and extinguishing.
這種「為」有生、住、異、滅的現象。

This means that it occurs when the karma is sufficient, then it maintains for a period of time, it starts to change when the karma begins to diminish, and it perishes when the karma is completely gone.
亦即：因緣具足時，開始產生，而後維持一段時間；當因緣開始減弱時，會產生變化；而當因緣完全消失時，就會滅亡。

In short, this 為 is impermanent.
簡言之，此「為」係無常的。

For example, the Great Wall.
譬若萬里長城。

For the sake of defense (因), a lot of people, materials and tools were gathered (緣), and then it's built. (生)
當初，為了防守（因），聚集眾多人民、材料、工具（緣）而建造了它。（生）

This is the 為.
這就是「為」。

It still exists. (住)
目前尙存。（住）

However, due to various reasons, it has been damaged. (異)
但因種種原因，已有損壞。（異）

Excuse me: Will it still exist 100 million years later? A trillion years later? (滅)
敢問：億年後仍在否？兆年呢？（滅）