Explanation please, of hardware and software serial links
Most small micro controllers, AVR's included, have dedicated hardware for communicating with different serial devices. In arduino these are referenced with "Serial", "Serial1", "Serial2" and so on, depending on how many hardware serial ports your particular arduino has. 

Leonardo's are an exception, the first hardware port is "Serial1" and "Serial" refers to the PC's usb connection. On the other arduinos that I know of "Serial" is hardware serial used for PC comms, so using it for other hardware requires sacraficing your PC link.

Software serial ports use the processors more generic pin-change interrupt system to communicate on any pins that support said interrupts, but they have a higher processing overhead and often cannot support the same high speeds as the hardware serial. There are different libraries for Software Serial that have different approaches giving different advantages and drawbacks.

To use a software Serial port you will need to make one to be used in your code, which will look something like this, depending on the type name the library you include uses:

SoftwareSerial softSerial( txPinNumber, rxPinNumber);


So in short, your processor has dedicated hardware for communicating over serial that should be used first, but if you need more ports the processor can simulate some extras which is referred to as "Software Serial". The documentation to your GPRS shield implies that either will work just fine. You should look at the arduino documentation for your board to see how many ports you have and which pins can be used for serial.

The documentation does not imply you will need any special link to your computer outside of the USB connection.