It suggests that something or someone meets the necessary requirements and is a good fit for the situation.
Here are some examples:
* "The new restaurant finally filled the bill for a good Italian place in town."
* "He's not the most experienced candidate, but he might fill the bill for this entry-level position."
* "This car doesn't quite fill the bill for a family road trip."
Essentially, "fill the bill" means something "does the job" or "is up to the task."