Rebbe Nachman of Breslov was a proponent of the view that one should rely on simple faith rather than intellectual sophistication, and avoid philosophical works. Here are some quotes from his works that explain his approach. They do not explicitly define simple faith, but they give you an idea of what he had in mind.
"Believe in God with pure, simple faith without trying to understand things philosophically. Most ordinary people may appear to be far from philosophy yet almost everyone is sunk in it to some degree. Even young children often have confusing theories.
Cleanse your mind and heart of philosophy. Cast it aside and pay no attention to doubts or questions: all you need is pure faith in God and the true Tzaddikim.
We received the holy Torah from Moses our Teacher. It has been handed down to us by outstanding Tzaddikim in every generation. We can rely on them without resorting to philosophical theories. Our task is to follow in their footsteps and believe in God with pure, simple faith, observing the Torah and its commandments as taught by our ancestors.
When a person is sincere and unquestioning, he can attain holy desire, which is even higher than wisdom. It is true that wisdom is higher than faith, but one must avoid sophistry and speculation, relying on faith alone. Faith has the greatest power. When you follow the path of faith, you can attain desire, which is even higher than wisdom.
One who attains desire experiences tremendous longing and yearning for God. The feeling becomes so intense that he does not know what to do, and he cries out...!!!
But there is a philosopher in man's heart. This is the Evil One, who puts doubts and questions into the heart. We must overcome this philosopher and drive him out, strengthening ourselves in faith alone."
Sichot Haran #32
"We believe in God with faith alone, not because of philosophical analysis .
We believe that He created the whole universe, that He sustains His universe and that in time to come He will renew it.
Philosophical works pose what appear to be extremely difficult questions while providing very weak answers. On further enquiry anyone can challenge the answers, which will be of no avail, merely generating more questions.
But the truth is that all their questions are nothing. They are mere vanity and striving after the wind. It is best to avoid such works completely."
Sichot Haran #40
"No sophistication is needed in serving God - only simplicity, sincerity and faith.
Simplicity is higher than all else. For God is certainly higher than everything else, and God is ultimately simple!"
Sichot Haran #101
"Even after all the wisdom and sophistication - even if you possess true wisdom - you must cast aside all wisdom and sophistication and serve God with complete innocence and simplicity, with no sophistication whatever.
The greatest wisdom of all is not to be wise at all. The truth is that no- one in the world is wise, for "there is no wisdom and no understanding . before God" (Proverbs 21:30 ) . The main thing God wants is the heart."
Likutey Moharan II, 44
"When a person follows his own mind and clever ideas, he can fall into many pitfalls and errors and come to great evil. Tremendous damage has been caused by such people , like the infamous great villains who , through their intelligence and cunning, have led the entire world astray .
The essence of Judaism is to conduct oneself in pure innocence and simplicity, with no sophistication whatever. Make sure that whatever you do, God is there. Don't heed your own honor. If it enhances God's glory, do it. If not, then don't. This way, you can be certain you will never stumble.
Be careful to act with true innocence and simplicity but not foolishly. Sophistication, however, is quite unnecessary. Simplicity, innocence and faith can bring you to the highest level of joy."
Likutey Moharan II, 12
"You should be careful to follow the simple devotions and customs of Israel: singing songs on Shabbat and at the conclusion of Shabbat, and similar practices. It is good to recite many prayers and supplications -- such as those printed in the large prayer books. People think it is clever to ridicule these practices. But they are wrong. The essence of Judaism is simplicity and purity, without sophistication at all."
Sichot Haran 155.