I'm following my professor's notes on QFT, and I cannot understand this passage. It's about an infinitesimal transformation for the coordinates of a scalar field $\phi$. The passage reads:

Let us consider an infinitesimal spacetime translation $$x^{\nu} \to x^{' \nu} = x^{\nu} - \epsilon^{\nu}$$ whence $$\phi_i (x) \to \phi'_i (x) = \phi'_i (x' + \epsilon) = \phi_i (x) + \epsilon^{\nu} \partial_{\nu} \phi_i(x)$$

I really don't get why he goes to $\phi'$ and I don't get the very last two terms of the equality (the scalar fields plus the derivative).

Can you help me?