It means that a person doesn't change.
Just like a tiger can't change his stripes to spots, triangles, etc. whenever he feels like it, every person has his or her own personal characteristics that are unchangeable, or at least very difficult to change.
For example, let's take Jim, who is always late to the office. One day, Jim says to two of his coworkers: "Tomorrow, I'm going to make sure to be on time for the big early meeting!"
After Jim leaves, one coworker turns to the other and says, "I don't believe it for a second. A tiger doesn't change his stripes."