Hi Shohadawy,
The first three terms are fairly generic ones;
In this context (ie Alarms), Active usually means an alarm condition that has triggered and is still present. Unacknowledge usually means it hasn't been 'Acknowleged' by an operator (not sure if this is a setting or a condition you are referring to). Remote acknowledge usually means you can use (say) the plc to acknowledge an alarm condition (eg set a bit), instead of going to the HMI directly and acknowledging on the screen.
Hope this helps.
Regards,
Rob