Just to increase vertical space between lines in cases by \\[1em]:
\[
\begin{cases}
f = -\dfrac {w_1*m + w_2*\frac{-d}{d_M}
+ w_3*\frac{r}{N} + w_4*s}{w_1+w_2+w_3+w_4}
& \text{when }m \geq t \\[3ex]% this increase vertical space between lines
f = -\dfrac {w_1*m + 5*w_2*\frac{-d}{d_M}
+ w_3*\frac{r}{N} + w_4*s}{w_1+w_2+w_3+w_4}
& \text{when } m< t
\end{cases}
\]
Result:

If you like to have more space, than increase distance between lines. I also suggest to \dfrac instead \frac or even better use the dcases environment instead of cases. To my taste equation will look better. For dcases you need to add package mathtools to preamble of your document, but no \dfrac is needed. Example:
\documentclass{article}
\usepackage{mathtools}
\begin{document}
\[
\begin{dcases}
f = -\frac {w_1\cdot m + w_2\cdot \frac{-d}{d_M}
+ w_3\cdot \frac{r}{N} + w_4\cdot s}{w_1+w_2+w_3+w_4}
& \text{when }m \geq t \\
f = -\frac {w_1\cdot m + 5\cdot w_2\cdot \frac{-d}{d_M}
+ w_3\cdot \frac{r}{N} + w_4\cdot s}{w_1+w_2+w_3+w_4}
& \text{when } m< t
\end{dcases}
\]
\end{document}

ex. (emis for horizontal measure.) but better still, try\openup\jotwhich increases the distance between lines in a math structure locally by 3pt. – barbara beeton Sep 29 '15 at 20:15openupis new to me. Where I can find some explanation about it? – Zarko Sep 29 '15 at 20:24dcasesenvironment is provided bymathtools, notempheq. The side conditions are better input as\text{when $m\geq t$}and\text{when $m<t$}. With thedcases*environment (again requiresmathtools) they can be input aswhen $m\geq t$andwhen $m<t$, because text mode is implicit after the&. – egreg Sep 29 '15 at 20:43empheq, notmathtoolsDoesampheqcallmathtools? About writing text incasesI agree with you, I just didn't bother with this. – Zarko Sep 29 '15 at 21:30empheq.stysays\RequirePackage{mathtools}[2004/10/10]– egreg Sep 29 '15 at 21:34empheqI will left to it to callmathtools:-) – Zarko Sep 29 '15 at 21:44