4.What do psychologists mean by the heritability of intelligence?

Intelligence is both a nature and a nurture thing. You inherit a certain amount of intelligence from parents. More intelligent parents tend to produce more intelligent offspring (ie from birth they are high on the Apgar, and perform age appropriate tasks either on or ahead of schedule). However, intelligence can be modified by environment. An intelligent child who receives little or no stimulation will not significantly increase its IQ, while one who is stimulated will do so.
This is not set in stone. Because genetics is inherited from a long line of people in ones ancestry, and things can go wrong in utero, very intelligent people can produce average or less than average intelligent children.

They are referring to the inheritance by a child of intelligence capacity from its parents.

ie: A baby born of genius parents would be more likely to also have a high IQ.

It has been somewhat proven that identical twins have similar IQs, but to confirm the aspect of the environmental influence, if both twins are brought up in different places, their IQ will be different. So somehow you do have a part of inheritance since you will be predisposed to better learning habits and personality, but the environment seems stronger than the inheritance on IQ test results. After all, the IQ test measures a PERFORMANCE at a given time, not someone's overall potential. So if the well predisposed person (genetically gifted) person is in a bad situation at the moment of the test, the environment will reflect more in the results. But it is still believed among experts that if "gifted" people are vs "not gifted" people in similar conditions at a given time, "gifted" people will "win".

genetically inherited.....genetics are passed down ,physically and mentally.....