Good communication means a lot of give and take: conveying information to clients and colleagues, and receiving incoming information with a full understanding of what’s needed or expected. Hiring supervisors who ask this type of question want to know about your clarity of thought, in both written and verbal exchanges.
Possible answer: Avoid giving an answer that says “I’m good at this, but not good at that.” Instead, talk factually about a communications-based task you did well—a report or a presentation before a group, for example. As for discussing “weaknesses in a job interview,” use the questions as an opportunity to focus on an actual strength (“I’m a stickler for detail”), or bring up an administrative weakness you had and how you overcame it (“I used to focus on one project at a time, but now I’ve learned to multitask”).