An input or output of an digital device is said to be high asserting when that input/output is considered to be "on", "active", "enabled", or "asserted" at the same time as the voltage present at the input/output is at the high level. Some ways of indicating that an input/output is high asserting:
enable(H)
enable[H]
enable

All these indicate that the input called "enable" is high asserting.

See also TTL, CMOS, low asserting.