"Specialized" organelles or parts means that these parts have been modified to carry out a specific function that is unique to them.
Organelles are literally "little organs" and each of them in the cell has a specific and distinct function.
For example the nucleus is an organelle. It is arguably the most important organelle in the cell. Its specific overall function is that it acts as the cell control center, directing the activities of all the other organelles .i.e. what they need do and when to do it.
The nucleus also contains all of the cell's genetic material (DNA).
