Why did God want a Tabernacle built by Moses? Is there a biblical basis why God wanted a Tabernacle to live among Israel (Exodus 25:8)? 


  And let them make me a sanctuary, that I may dwell in their midst.  Exodus 25:8 ESV


What is the significance of the Tabernacle built by Moses?
To accomplish God's desire to make his abode among his people, [...]. He wanted to walk among them, be their God, and they his people1.

1. cf. Lev 26:11-12 (RSVCE).

Please see also this Moses' intercession [cf. Exod 33:14-16]:


  14 And he said, “My presence will go with you, and I will give you
  rest.” 15 And he said to him, “If thy presence will not go with me, do
  not carry us up from here. 16 For how shall it be known that I have
  found favor in thy sight, I and thy people? Is it not in thy going
  with us, so that we are distinct, I and thy people, from all other
  people that are upon the face of the earth?”


Summarizing the reasons that appear:


It was God's wish.
So that God might make his abode among his people, walk with them and be their God, and they his people.
In response to Moses' intercession.
God's continual presence would distinguish his people from all other people.