I've always wondered what discrete and continuous mean in mathematics? I couldn't make out the difference between them for long. But here are two plain explanations:

1. The adjective "discrete" [in discrete mathematics] is the opposite of continuous. roughly speaking, objects in discrete mathematics, such as natural numbers, are clearly separated and distinguishable from each other and we can perceive them individually -- like trees in a forest which surrounds us.

In contrast, for a typical "continuous" object, such as a set of all points on a line segment, the points are indiscernable -- like the trees ina forest seen from a high-flying airplane.

1. The adjective "discrete" [in discrete mathematics] is the opposite of continuous. roughly speaking, objects in discrete mathematics, such as natural numbers, are clearly separated and distinguishable from each other and we can perceive them individually -- like trees in a forest which surrounds us.

In contrast, for a typical "continuous" object, such as a set of all points on a line segment, the points are indiscernable -- like the trees ina forest seen from a high-flying airplane.

---- Invitation to Discrete Mathematics by Jiri Matousek and Jaroslav Nesetril

2. continuous -- a property of things that can be divided into infinitisemal parts, which include geometric objects such as lines, surfaces and the the three-dimensional space we live in

discrete -- describing things that come in whole indivisible parts, such as the whole numbers.

---- Plus Math

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