In a series circuit there is only one path. The same current passes through each resistor in turn, and each one opposes the flow of charge. Adding another resistor in series means the charge has more to push through, so the net resistance increases. The net resistance is the sum of the individual resistances.
In a parallel circuit the current has more than one path. Each branch is connected directly across the cell, so each has the same potential difference. Adding another branch gives the charge an extra path to flow along. More current flows from the cell for the same potential difference, so the net resistance decreases. It ends up smaller than the smallest single resistor.
You can see this with bulbs. Two bulbs in series are dimmer than one bulb because the current is lower. Two bulbs in parallel are each as bright as a single bulb, because each has the full potential difference of the cell.
