Welcome to Biology.SE!
from one generation to another is equivalent to
from parents to their children
from any parent generation to any offspring generation
If the expression
from one generation to another really bothers you, then you can just consider the shortened sentence which bear the same meaning.
Genetic traits are the traits that are carried from parents to their children
One reason why there is this reference to generations is because it is common in population genetics models to assume for simplicity that generations are not overlapping. That is all parents reproduce only once and all die at this exact same time. As such an offspring is never alive in the same time as the parent. It is an unrealistic model for most species but it is a very helpful one.