This is my personal understanding of the issue. A more complete and sound answer can be found here (you should probably use translators if you cannot read in Persian/Farsi)
First of all, in the common Shiʻite view of the Shia scholars, Aql is not only a source of Fiqh, but it is the only way we have when we are at a point to accept/reject Islam before to become a Muslim/Kafir. (Note This Aql is not something more related to the brain, like is thinking and logic, but it is more related to heart, although this fact is largely ignored some times)
Next, about Aql as a source of Fiqh. A simple example is that if something is obligatory in Islam, preparing the conditions to be able to behave according to that obligation is also obligatory, intellectually. For example, I know that I must get up early in the morning for the morning prayer, and I know that if I go to sleep late in the night, then it will be certain that I will miss my prayer. So intellectually, it is forbidden for me to sleep so lately. This is not that simple though in the words of scholars, as it has many problems involved that needs consideration, so for a more thorough answer you should read books, or ask due scholars, I'm not the one that can help.
Another example can be the fact that if doing something obligatory, does it necessarily mean that not doing that is always forbidden. For example, telling lie is forbidden, but telling the truth is not always obligatory.
Another example, which I didn't find in the link provided above, but I guess to be a proper example, is when different rules of the religion yield into a dilemma. Not all such situations are addressed in Quran and the reliable Ahadeeth, so maybe it will be a serious application of Aql in identifying what Allah expects from me to do. By the way, this is called Hikmah (a global knowledge as a whole, compared to local knowledge of the rules individually) in some Ahadeeth.
Last but not least, let me add that Aql being a source of Fiqh is both
on Quran and Ahadeeth as well, though somewhat implicitly (if you
conduct a study on the real meaning of Aql, you may conclude that the
references in Quran and Ahadeeth are rather explicit indeed). For
وَنَفْسٍ وَمَا سَوَّاهَا ﴿٧﴾ فَأَلْهَمَهَا فُجُورَهَا وَتَقْوَاهَا ﴿٨﴾
قَدْ أَفْلَحَ مَن زَكَّاهَا ﴿٩﴾ وَقَدْ خَابَ مَن دَسَّاهَا ﴿١٠﴾
By the Soul, and the proportion and order given to it; (7) And its
enlightenment as to its wrong and its right;- (8) Truly he succeeds
that purifies it, (9) And he fails that corrupts it! (10)
بَلِ الْإِنسَانُ عَلَىٰ نَفْسِهِ بَصِيرَةٌ ﴿١٤﴾ وَلَوْ أَلْقَىٰ
Nay! man is evidence against himself, (14) Though he puts forth his
There are much more things about Aql that can be said, but this much should suffice as for the beginning.
Hope that it helped.
EDIT to answer OP's comment here, as it was not a proper fit to comment area:
@Medi1Saif, actually both yes and no. If Aql is something from my own side (like thinking apparently is), its wrong to use it to go by, since "إِنِ الْحُكْمُ إِلَّا لِلَّـهِ", that is, "the command is for none but Allah". Although even if so, one may exploit "لَا يُكَلِّفُ اللَّـهُ نَفْسًا إِلَّا وُسْعَهَا", that is, "On no soul doth Allah Place a burden greater than it can bear".
But why no, because Aql resides in Heart: "لَهُمْ قُلُوبٌ يَعْقِلُونَ بِهَا", that is, "have hearts by which to reason", while for some people "تَعْمَى الْقُلُوبُ الَّتِي فِي الصُّدُورِ", that is, "blinded are the hearts which are within the breasts".
those people who suffer disease in their heart "فِي قُلُوبِهِمْ مَرَضٌ", if they think they are using their intellect, they may go astray instead of getting survived. This is why in Shia there is a famous saying that, what ever Aql rules, is a rule of Allah, and whatever Allah rules, is something that Aql accepts (کلما امر ب العقل امر به الشرع، و کلما امر به الشرع امر به العقل). And there is a Hadeeth from Imam Hussain PBUH that go by religious rules, so that your intellect recover from its diseases and incompletenesses.
Those who can safely use their Aql, are actually those who have قلب سلیم, "إِلَّا مَنْ أَتَي اللَّهَ بِقَلْبٍ سَلِيمٍ", that is, "But only one who comes to Allah with a sound heart"
What usually people mean by Aql is different, they at most try to think logically, and sometimes they conclude the opposite of the rules of Allah, that's a place where Allah says "مَا أُوتِيتُمْ مِنَ الْعِلْمِ إِلَّا قَلِيلًا", and "ذَلِكَ مَبْلَغُهُمْ مِنَ الْعِلْمِ" and "وَ مَا يَتَّبِعُ أَكْثَرُهُمْ إِلَّا ظَنًّا إِنَّ الظَّنَّ لَا يُغْنِي مِنَ الْحَقِّ شَيْئًا".