There are multiple origins and meanings for the name Layla:
1. Arabic name (ليل) meaning - "night, nightly, born at night, dark-haired beauty, dark beauty". See the name Leila.
Layla and Majnun is a classical love story. It is based on the real story of a young man called Qays ibn al-Mulawwah (Arabic: قيس بن الملوح) from the northern Arabian Peninsula. In one version, he spent his youth together with Layla, tending their flocks. In the other version, upon seeing Layla he fell passionately in love with her. In both versions, however, he went mad when her father prevented him from marrying her; for that reason he came to be called Majnun Layla, which meaning - "Driven mad by Layla".
2. Hebrew name (לַילָה) meaning - "night, darkness".