Miracles defy the laws of the natural world and challenge the most basic premise of science. Sciences systematize knowledge relating to the physical world and try to establish verifiable laws. An observation incompatible with a commonly accepted scientific principle is understood to demand a replacement theory.
Many people are comfortable with the notion that the processes of nature are fixed, and resolve the phenomenon of miracles with the explanation that the Creator Who established the laws of nature is powerful enough to alter them temporarily.
Many scientists who maintain that the unchanging character of laws of nature is a reality that cannot be tampered with reject this approach.
There is, however, a different perspective on miracles, which is simultaneously more profound philosophically and more palatable, scientifically.
It is universally accepted that the world operates in cycles and fixed patterns. The believer asserts that Hashem’s modus operandi is to create, whatever He creates, in an orderly, organized fashion, in which systemic laws are as unchanging and eternal as His name.
Every miracle, then, is part of a system, a system, distinct however, from the one that we recognize here on earth. Miracles are the laws of an order governed by different dictates, part of a system governing the spiritual world. Therefore, it is unnecessary, and perhaps even erroneous, to consider miracles a deviation from the natural order that Hashem set in motion.  Rather, a miracle is part of a parallel system designed by Hashem, in which different principles apply. 
Since events in the spiritual world correspond to events in the physical world, our existence here interacts with both systems.
The first system consists of the laws of science with which we are familiar; the second system is the arena in which nature actively responds to the Jew on a personal and communal level. In the spiritual world, success is a direct response to our positive behavior and our close connection to Hashem, a blessing showered on the Jewish people. Estrangement, in contrast, is manifested in trouble and tragedy. (Of course, life is not so simplistic and people may suffer or prosper for other reasons.)
We are generally not privy to the second system since such awareness would neutralize our free will and obviate the point of this world. Nonetheless, it exists and is recognizable to the trained eye.
On rare occasions we get a glimpse of the second system as we witness a miracle. Parshas Beshalach revolves around such miracles, including the splitting of the sea exactly at the right moment, as well as the provision of the mon. The people benefited from the spiritual system as a matter of course, since they were on a journey in search of spirituality and connection to Hashem. The miraculous aspect is the revelation of the normally hidden realm – the spiritual world – in the midst of the physical world. The classical miracle generally displaces the laws of nature.
Interestingly, both systems sometimes function simultaneously. During the plague of blood the same cup was water for the Jew and blood for the Egyptian.  During the battle at Givon, the sun stood still for Yehoshua but for the rest of the world the earth continued its normal rotation and no time was lost. 
Since every miracle is a window to the spiritual world, it is the perfect tool for heightening our awareness of our noble role in the universe and facilitating recognition of how important we and our actions are to Hashem. Every so often we are glaringly exposed to a scene from the spiritual realm in which Hashem is obviously focusing on and responding to us. It is helpful to bear in mind, though, that it is not an evanescent display; rather we have peeked into a whole world devoted to tracking and caring for Bnei Yisrael.
No wonder that the belief in miracles is fundamental to Judaism.
With this approach, although miracles do defy the laws of the natural world, they do not challenge the premises of science. Rather, miracles are meant to expand our awareness of the vastness of creation to encompass another realm with its own distinct system.
מקורות: אגרת הרמב''ם על תחיית המתים ומהר''ל בגבורות השם בהקדמה שניה.
 Even some Jewish philosophers ((קדמונים, while accepting the reality of miracles, express difficulty in understanding them. They view any change in the order of nature as an indication of an unstable and imperfect original creation, which reflects negatively on the Creator. The Maharal defends this argument. (Source cited at the end of the article).
 כי בי-ה הויה צור עולמים, כל הנבראים נבראו בשמו יתברך, וכמו ששמו קיים נצחי כך ראויים מעשה בראשית התלויים בשמו להיות נצחיים. מהר''ל.
 הקורא הלל בכ''י הר''ז מחרף ומגדף (שבת קי''ח:), מפני שהוי כאומר שאין סדר בעולם אלא הכל נוהג בלי סדר. מהר''ל.
 וזמש''כ בשמו''ר כא.ו. תנאי התנה הקב''ה עם מעשה בראשית שיבקע הים, וכן בשאר הנסים, כלומר, דגם סדר הניסי הוא חלק מהבריאה מעיקרו ואי''ז שינוי בסדרי הבריאה.
 יג תנחומא וארא
 יהושע פרק י'
 That is why miracles only happen to or for Klal Yisrael