A soft synth (software synthesiser) is a computer program, which may be either standalone or a plug-in, which recreates the functions of a traditional hardware synth. So it will generally have virtual recreations of oscillators, filters and envelopes, usually as well as a ton of other stuff. I don't believe either Garritan or Vienna would be considered soft synths; instead of actually creating the audio in real time, they simply play back pre-recorded samples of instruments. Though I could be wrong.
A hardware synthesiser isn't, as Connor said, a keyboard you connect to a PC (some hardware synthesisers aren't even controlled by keyboards). A hardware synthesiser has the physical versions of the components found in a soft synth, and actually creates the sound itself, whereas a physical keyboard connected to a PC would usually be a MIDI controller, which you could then use to control things such as soft synths or samplers. MIDI controllers create no sound by themselves, but are used as a means with which to control other things that do - it's often far easier, for example, to use a MIDI controller with sequencing software rather than inputting each note individually with a mouse and keyboard.
I think that's all right, anyway.
