In the name of God the most gracious, the most merciful.
My understanding of a miracle is anything that cannot be explained through natural process.
There are many miracles I could mention, but I'll stick with one, the well of Zamzam. If you want to find more miracles, just google the miracles of the Qur'an.
As for the well of Zamzam, it's a well in Makkah, close to the Kabbah, according to Islamic sources, as well as Genesis 21:17-19 and Psalms 84, Zamzam was dug up when Prophet Abraham (peace and blessings be upon him) left Haggar and their baby boy, prophet Ishmael (PBUH) in the middle of the dessert, fulfilling God's command, and while Haggar was there, she ran out of food and water and had to look for help, she left her baby and ran up and down near by hills until suddenly she saw a little well of water next to her baby. Arab tribes started gathering around this well and eventually the city Bakkah (now Makkah) was formed and Abraham and his son Ishamel built the Kabbah as a command from God. Until this day, even though all wells around Makkah have dried up, the well of Zamzam remains, as a sign of God's mercy upon mankind.
Say, "O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allah. Indeed, Allah forgives all sins. Indeed, it is He who is the Forgiving, the Merciful." (Qur'an 39:53)