It's a very common and important word in Arabic, used in many contexts, such as:
* Daily life: "Hayat al-yawmiyya" (حياة اليومية) - daily life
* Human life: "Hayat al-insan" (حياة الإنسان) - human life
* The afterlife: "Hayat al-ākhira" (حياة الآخرة) - the afterlife
* Living things: "Al-hayawanat al-hayya" (الحيوانات الحية) - living animals
The word "hayat" itself doesn't have any specific connotations beyond its core meaning of life. It's a neutral term that can be used in a wide range of contexts.