Same current flows through 2 resistors in series. (Think of it as a water stream and follow it through the circuit).
Since (voltage across a resistor) = (current that flows through a resistor, I)X(resistance of the resistor, R), for a series connection I is the same and R may or may not be the same, hence voltage drop is proportional to resistance (bigger one will have a bigger voltage across it).
In a parrallel connection, "the water stream" splits into 2 or more possible paths. Different current flows through different paths. Voltage across each resistor is the same (because voltage is defined as potential #1 - potential #2) and since multiple resistors are connected to the same 2 points the difference in those 2 potentials and thus voltage is the same. current is not however, more current will flow through the "less resistant" branch. Think of a inf Ohm resistor as an open circuit and 0 Ohm resistors as a short cirtuit/wire.