Question

What does it mean to connect a circuit in parallel versus series?

Answer 1

Below picture is the easiest explanation.

Resistors R1 and R2 are connected in series, whereas R3 and R4 are in parallel.

For the current it means that the current through R1 and R2 is always equal, which is not the case for R3 and R4, there the current splits depending on the R value.

For the voltage it means that the voltage over R3 and R4 is always the same, regardless of the R value.