I think what you're looking for a is a virtual instrument or virtual instrument plug-in or VSTi (technically that is a specific kind of virtual instrument, but some people use the word as a catch-all).
A virtual instrument takes MIDI input and provides audio (sound) as an output. Usually a virtual instrument is used as a plug-in inside of host software or a DAW. Both refer to larger programs that can record and sequence audio and MIDI information, as well as provide input and output functions for MIDI and audio streams.
A typical way to use a virtual instrument in a DAW is as follows:
- Create a new track in the DAW - some DAWs have different types of tracks, and the track type you would want for a virtual instrument might be called "virtual intrument", "instrument", or possibly a "MIDI" track.
- Insert the instrument plug-in into the new track. Each DAW has its own process for inserting plugins.
- Change the MIDI input routing settings on the track to connect your MIDI controller to the virtual instrument. When using USB MIDI, if the drivers and operating system settings are in place, usually the name of the MIDI controller will show on the list of MIDI sources to choose from.
- Check and/or change the output audio routing for the track to send the output to an output bus, mix bus, aux bus, aux return, etc. Usually an output bus lets you hear the audio in real time and an aux bus or mix bus lets you record the audio (and also hear it in real time as you record).
It can take a bit of fiddling around to get the whole thing working because there are so many combinations of DAWs, virtual instruments, interfaces, and controllers, all which have to work together to make it work.
There are thousands of virtual instrument plugins available. Many online retailers have entire sections of their virtual store devoted to them:
https://www.sweetwater.com/shop/computer-audio/plugins/
http://www.guitarcenter.com/Virtual-Instruments-Software.gc
http://www.musiciansfriend.com/virtual-instruments-software
Also, some DAWs include a selection of virtual instruments to get you started.