A subset is a set that is contained in a larger set.
A “set” is simply a collection of elements. These elements may be physical objects, such as the people in your family; or abstractions, such as numbers. The elements in a set may themselves be sets.
There is a fairly simple notation for sets. We simply list each element (or "member") separated by a comma, and then put some curly brackets around the whole thing: {socks, shoes, watches, shirts, ...}; {index, middle, ring, pinky}.
When we define a set, if we take pieces of that set, we can form what is called a "subset".
Example: the set {1, 2, 3, 4, 5}
A subset of this is {1, 2, 3}. Another subset is {3, 4} or even another is {1}, etc.
But {1, 6} is not a subset, since it has an element (6) which is not in the parent set.
In general: A is a subset of B if and only if every element of A is in B.
So what does this have to do with mathematics?
Sets are the fundamental property of mathematics. Now as a word of warning, sets, by themselves, seem pretty pointless. But it's only when we apply sets in different situations do they become the powerful building block of mathematics that they are.
Math can get amazingly complicated quite fast. Graph Theory, Abstract Algebra, Real Analysis, Complex Analysis, Linear Algebra, Number Theory, and the list goes on. But there is one thing that all of these share in common: Sets.
Learn more about sets on MathsisFun.com and DecodedScience.org.