This award winning web site Panorama - applications of mathematics by Philipp Legner is very well done and could be the type of resource you would direct someone to who asks "what is the use of mathematics?".
Everything in our world follows mathematical laws: from the motion of stars and galaxies to the transmission of phone signals, bus timetables, weather prediction, and online banking. Mathematics lets us describe and explain all of these systems, as well as revealing profound truths about the underlying patterns.
The items are organized by type of math (algebra, geometry, calculus, statistics, graph theory, number theory) and type of application (technology, engineering, media, sports, medicine, finance, nature). Nothing goes very deep, but there are pointers to "enrichment sites" and also to career sites. And there's also humor, Mystic Mathematics, for the math of computer games, is my favorite.