First of all, I like the title of the question, "What makes a circuit Digital" ;). The world around us is analog so the electronics started with exploring the analog components like the ones mentioned by you resistors, capacitors etc. read more
If a circuit is said to be digital, outputs of circuits are either 1 or 0. So in an electric circuit if steady state outputs are either VDD(power supply) or 0(gnd) then one can refer it as a digital circuit. read more
An electronic circuit can usually be categorized as an analog circuit, a digital circuit, or a mixed-signal circuit (a combination of analog circuits and digital circuits). Breadboards, perfboards, and stripboards are common for testing new designs. read more