A miracle is defined by the Catholic Church (and I don't see where their definition differs that much from other faiths) as "wonders performed by supernatural power as signs of some special mission or gift and explicitly ascribed to God." (see Catholic Encyclopedia at www.newadvent.org)
Miracles, then, are unnatural, wonderful occurrences and the hand of God can be clearly seen in them. I think, generally speaking, that people ascribe God's will to things that they can't otherwise understand, as in someone beating a disease, or getting a promotion at the time you need it most financially, or some other extraordinary event. I understand this, and will never take anyone to task on this belief, but it's not really one that I share. Wonderful things happen, but whether we identify them as miracles or not ultimately comes down to, like most things, personal faith. As I said, I certainly understand the need of some people to believe in them.