Laylat Jizra/ Lailatul Jaiza [lay-lat jiz-rra] or the 'Night before Eid' is known in English as the 'Night of Reward'.
The following example of writing, which explains the meaning of this particular night, has been endlessly copied throughout the blogging world and the websphere. I'm doing the same for this particular post; copy and paste but have removed some parts with the aim of making it easier to understand for non-Muslims:
“It had been the practice of the Prophet that he would not sleep in the night preceding the day of Eid-ul-fitr. This night has been named as the Night of Reward. Almighty bestows his rewards on those who have spent the month of Ramadan abiding by the dictates of Shari'ah, and all their prayers in this night are accepted.
The Prophet is reported to have said:
Whoever stands up (in worship) in the nights preceding the two Eids expecting rewards from his Lord, his heart will not die when the other hearts will die. (Ibn Majah)
To benefit from this opportunity one should perform as much worship in this night as he can, and should pray for all his needs and desires."