typedef bool (OptionManager::* OptionHandler)(const ABString& value);
Let's start with:
OptionManager::* OptionHandler
This says that ::* OptionHandler is a member function of the class OptionManager.
The * in front of OptionHandler says it's a pointer; this means OptionHandler is a pointer to a member function of a class OptionManager.
(const ABString& value) says that the member function will take a value of type ABString into a const reference.
bool says that the member function will return a boolean type.
typedef says that using "* OptionHandler" you can create many function pointers which can store that address of that function. For example:
OptionHandler fp[3];
fp[0], fp[1], fp[2] will store the addresses of functions whose semantics match with the above explanation.