@Baka is along the right lines but @Jonh is right to note different contexts.
I come from a geological background, so to me a mineral is basically the different crystalline components of a rock. Rocks are made of multiple minerals. if you break a mineral down, you end up with atoms. Eg. Quartz is a mineral, it can be found in granite (a rock), but if you break it down further you get silicon and oxygen atoms.
In my experience when gardeners talk about minerals, they are talking about the ions produced by the breakdown of minerals. So for example, feldspar (another common granite mineral) will eventually break down (via various clay minerals) to release Iron, Magnesium, Potassium, Sodium, Calcium, and Aluminium (not all of these are present in all feldspars). This list of elements in ion form, are what the gardeners are talking about as minerals.
Perhaps a proper chemical definition might be "ionic nutrients"? This would include the above cations (essentially metal ions), mineral-derived anions (eg. some phosphate), and the soil/manure derived anions (eg. phosphates from guano; nitrates from nitrogen fixing and manures).
(Ions are charged atoms that result when a salt dissolves. eg. Potassium Nitrate would give you Potassium ions and nitrate ions)