I'm sure what your manual meant to say is that your clock is accurate to within plus or minus 3 seconds a month. The accuracy of the clock is dependent on the hardware.
On HP systems a technician can adjust the accuracy of the clock if it is way off. But +/- 3 seconds/month is not bad.
For greater accuracy, you can run NTP, a networking service that keeps your clock in sync with super accurate network visible clocks. That will keep you to within a second very easily.
The official unix standard demands that the seconds of a minute be within the range 0 to 59 and each day must comprise exactly 86,400 seconds. This allows you to precompute the number of seconds between two times in the future. But it also means that leap seconds are illegal. So a strictly conforming unix system must be off by one second every now and then. However, it is common to violate the prohibition against leap seconds. This is the only constraint on clock accuracy that unix attempts to impose.
See
this thread.