I really tried to understand the wikipedia page but… Tangent space - Wikipedia
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A tangent is directly related to it bi-tangent and a normal.
A normal of course as your aware is the direction a meshes face faces in orthogonality (viewing it straight on, no perspective).
A tangent vector is a vector that lies on the surfaces plane or which lies tangent (remember cos,sin,tan?) to a single point (like an imaginary vertex) on a curved surface. So. If you had a single plane mesh in UE4 and the normal was your reference point, the tangent vector would be co-planer to the plane.
A bi-normal tangent vector is usually orthoganel to both a normal and the tangent point youve chosen as a reference point at least in computer graphics.
These are not specific points per say, they are available every single pixel in 3d space.
See this wonderful drawing as close as ELI5 will get. Normals are a complicated subject, trigonometry hurts my head enough.
http://i.stack.imgur.com/tAQNN.png
Of course you can view them in UE4 with your own meshes to get a better sense of what htey look like especially now that we have proper tangent space.
Hope this helps
Don’t forget to accept an answer that best clears your question up or answers it so when the community finds your question in the future via search/google they know exactly what you did to fix it/get it going.
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Thanks! 
That made things much clearer.
For everybody still wondering what tangent space in UE4 is, here are some more resources i found:
http://docs.cryengine.com/display/SDKDOC4/Tangent+Space+Normal+Mapping
and
http://wiki.polycount.com/wiki/Normal_Map_Technical_Details#Tangent-space_normal_map
there are also some good explanations in a reddit thread I started with the same title:
https://www.reddit.com/r/unrealengine/comments/3jybcl/eli5_what_is_tangent_space_in_ue4/
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