Most of us are actually experiencing that our computer is intelligent
We feel the computer helps us when the spell-checker in our word processor informs us about our spelling errors, and even too suggests alternative formulations when we are floundering in the grammar. We are overwhelmed when the map tool gives us a driving directions from one place to another immediately. And we are helped when the planning system on the computer puts together a schedule of many people's work.
In all such cases it is complicated methods in the software running on your computer, that is making these clever things. These calculation methods - language features, route directions, plannings, etc. - are as in general called algorithms.
The more sophisticated algorithms built into the software, the more advanced work the software can do for us. It is the algorithms in the software that makes us to experience that the computer is intelligent.
Many of us have also though experienced computer programs, which presented us with an overflow of technical details, and asked us to consider a lot of unnecessary things. And although the task the computer solved for us might be very complicated, we did not experience that the computer solved the task in a clever and wise way.
The good algorithm makes everything look easy and simple