Alief, pronounced "ah-leaf," is a way of describing what someone instinctively thinks or feels, even if they don't necessarily believe it to be true on a conscious level. It's kind of like what your brain automatically thinks or feels about something before you have a chance to really think about it.
For example, if you see a scary spider, your initial alief might be that it's dangerous and you should run away, even if you know in your head that it's not really going to hurt you. Another example might be if you hear a loud noise in the middle of the night, your alief might be that it's a monster even though you know logically that it's unlikely to be true.
So basically, alief is like a knee-jerk reaction or gut feeling that you have about something, even if it doesn't necessarily line up with what you actually believe to be true.