Here are some examples of how it can be used:
* "I've got a few questions for you to chew on. What are your thoughts on the company's new strategy?"
* "That's a lot of information to take in. Chew on it for a bit and we can discuss it further tomorrow."
* "Before you jump to conclusions, chew on that information for a while. There might be more to the story."
The phrase comes from the image of someone chewing on a piece of food, taking their time to digest it. Similarly, when you "chew on" an idea, you're taking time to fully understand and process it.