I'm given this

$\displaystyle \frac{\phi{(x + \delta{x})} - \phi{x}}{\delta{x}} \approx \frac{d\phi}{dx}\mid_x + O(\delta{x})$

Hence

$\displaystyle \delta{x} = \phi{(x + \delta{x})} - \phi{x} = \frac{d\phi}{dx}\mid_x\delta{x} + O(\delta{x}^2)$

I dont really understand either of these statements especially where O comes from and why you need it. Anyone have any ideas or know anywhere to point me where i could get an explaination