You have a sorted array, and you start looking at midpoints to converge on the region that has the element you are looking for.
This is an intuitive way of how we get logarithmic complexities, by dividing the input space by two at each iteration, it means the total effect is the oposite of exponentiation, that’s called logarithmic. ie n elements, go down to n/2, n/4, n/8, … how amny steps until you get to 1? log(n) literary means 2 to the power of what gives me n?