In a DC parallel circuit, equal voltage is applied to each device that is connected in parallel. For example, if three devices are connected in parallel to a 9 volt battery, each device will have 9 volts applied to it.
In a DC series circuit, the sum of the voltage drops across each device connected in series equals the source voltage. So say you have three devices connected in series, and they are connected across a 9 volt battery. Each device will have less than 9 volts across it, but if you add the voltage drops across each device togther, it will equal 9 volts.
Batteries in series have an additive effect to the voltage. A single AA battery has 1.5V. Two in series will have 3.0V. Batteries in parallel do not experience an additive effect to voltage.
To answer this question briefly there is a big difference. The major difference is the resistance the circuit offers when the same components are wired in series or parallel. I do not know how much you want to know, but resistance of a component is measured in Ohms. An easy way to think of ohms is how much force or energy is required to move an object. The less ohms a circuit has the more it can do with the same amount of energy, which in some cases can be a bad thing. To move on, lets say you have two light bulbs, to give a cliche example, and both are 2 ohm load. Now if you wired these two light bulbs in series, connect positive of one bulb to negative of the other and then the others to a battery, the bulbs would be half as bright as one bulb to the same battery. Yet if you wired these in parallel there brightness would be the same as if one light bulb was connected to the circuit. This is because the voltage in the parallel circuit doesn't decrease when you add a light bulb, whereas on the series circuit it does decrease. Hope that helps