# Why consumption is defined as $C_t:= \left(\int^1_0C_t(i)^{\frac{\epsilon-1}{\epsilon}}di\right)^{\frac{\epsilon}{\epsilon-1}}$

I am reading Monetary policy, inflation, and the business cycle: an introduction to the new Keynesian framework and its applications by Gali.

In section 3.1 he presents/defines the consumption as $$C_t:= \left(\int^1_0C_t(i)^{\frac{\epsilon-1}{\epsilon}}di\right)^{\frac{\epsilon}{\epsilon-1}}$$

$$\epsilon$$ is the elasticity of substitution and $$i$$ indexes the goods available for consumption. It is related to the New Keynesian Model.

Can someone give me verbal explanation of why it make sense to define the consumption this way?

$$C_t(i):$$ How should interpret the $$i$$-line?

$$i$$ indexes the goods available for consumption