Is intelligence (or mental ability) genetically transferred (inherited characteristic) from the parent to the offspring or is it an acquired trait?
Standard IQ test are often considered the best proxy for intelligence. Studies show IQ heritability varying between 0.5 (ref) and 0.8 (ref).

TO make sense of these numbers, you will need to understand the concept of heritability. You can find info on this important concept in the post Why is a heritability coefficient not an index of how “genetic” something is?. Other posts also offer an intro to this concept (see this, this, this or this post). You can also simply have a look at wiki. You might want for example to be able to understand the equation $H_N^2=\frac{V_A}{V_P}$ without further explanations.

The H2DB database may interest you as well and of course the wiki page on heritability of IQ