What if I choose replacement tires narrower than my current tires? I have been looking for some tires I could buy but I couldn't find exact numbers (My current tires are 27.5 x 2.8)

I found one which was 27.5 x 2.10 or should I get one which is 27.5 x 2.1 Both of them are the same price but I don't know which one to get, can you please tell me?
2.8 is bigger than 2.10. 

When you run a bigger tire, you have to worry about the tire rubbing on the frame or fork.

Running smaller tires are usually simpler.

Tire sizes have to be appropriate for the rim width; wide tire on narrow rim could have some control issues/sloppiness (and if you had rim brakes, that could also cause some rubbing). Narrow tire on wide rim could increase risk of damage from hazards. See this page for details: http://www.sheldonbrown.com/tire-sizing.html