Example 1: At first, the new-hire wasn't sure about his co-workers; but now that he has gotten to knowthem, he enjoys their company.
Example 2: When you arrive in a city for the first time, traveling around and finding new things is usually difficult. Once you get to know the city, however, everything becomes much easier.
Meaning: "To get to know" suggests that something that was unfamiliar or "unknown" becomes familiar or "known." "To become familiar with" is a synonym.
"To get to know" is an idiom found in unit 4 of Reading Transitions, a Language Systems International text book used for Level 4 students.