Roads one mile away from the General Post Office would have a stone saying "one mile". Likewise there would be "milestones" at various points two miles away from Post Office, and so on. The granite marker below (recently discovered) represents a point on a road that was three miles (around 4.8km) away from the post office.
Example of a Singapore milestone (source).
By now, you should be guessing that Bukit Panjang's Ten Mile Junction gets its name from the fact that it was ten miles away from the GPO.
This Straits Times article gives more information. Click on the below picture for an interesting map which shows the location of all previous milestones!
Jerome Lim has published an excellent article about such milestones, which includes a photo of the 13.5 milestone marker at the old Sembawang Gate.
