Nowadays, people like to have reliable weather forecast for the day; they also like to have more powerful computers that are cheaper, cars that are nicely designed, reliable, and loaded with safety features and that have good mileage. Boeing, when it unveiled it newest airliner, the Boeing 777, said that it was the first completely "paperless" major commercial transport design, see the article in American Scientist for further details. Also, if you want to get a better idea of what scientists and engineers do to design planes, go to the MIT web site. Why do all those things happen? Because of mathematical modeling and the more powerful computers.
Mathematical Modeling is an interdisciplinary subject bringing together mathematicians and specialists in other fields to improve existing products, develop better ones, or predict the behavior of certain products and how things will be in the future. These people share their knowledge and expertise to improve your every day life.
How do they do that? For example, to improve the design of a product, the interdisciplinary team first lists all the requirements the product needs to meet. It also uses the data from experiments or tests to find simplifying assumptions and translate the physical phenomenons into equations. Then, the derived equations are analyzed, solved, and the qualitative or numerical solution is interpreted. The simplifying assumptions and the computed solution are validated against the data. If, the data and the computed solution are not a good fit, some of the simplifying assumptions are relaxed and the model is improved. The analysis, solution process, validation, and relaxation of the simplifying assumptions cycle is repeated until there is a good agreement between the solution of the model and the data (note that "good agreement" is a rather vague statement and the team will decide what it means based on the problem considered and the specialists in the field's experience.) With the more powerful computers, modeling teams have been able to tackle more complex problems, develop more accurate models, get answers in less time, and reduce research and development costs.
So even though you do not have the impression that mathematical modeling does improve your everyday life, it does. You can buy better products at less cost and you can get things done faster.