In the context of schematics:
A 'net', short for 'network', is a collection of interconnected points (pins on ICs, discretes, passives, connectors, etc.)
A 'line' is a drawing element showing a connection between a pair of points in a network.
Schematics can visually represent nets in a number of different ways:
- connected by lines pin to pin
- connected by junction (dot, tee) between lines
- connected by name to the same net
- connected as part of a multi-signal bus
- connected by off-page ports to other pages (multi-page drawings)
- connected by ports to other modules (hierarchical drawings)
- automatically connected hidden power/ground - not recommended
The schematic tool scans the drawing and finds these connections and compiles them into a series of lists: each identified net, and the pins each net contains. (The tool will automatically assign a unique net name to each net even if you didn't assign one yourself.)
This list-of-nets information - called, oddly enough, the netlist - is what is used later to make the board layout.