VoIP is an acronym for Voice over Internet Protocol or as commonly stated Voice over IP. Internet Protocol (IP) is the method by which data is sent over the Internet (from computer to computer for example). So, basically, VoIP is the transmission of your voice over an internet connection.   

As VoIP uses your internet connection to transmit your voice (analog) over the internet (digital), your voice signal must first be converted into a digital signal that the Internet Protocol (your internet connection) understands. This digital signal of your voice then travels over the internet and is directed to the number you are calling. At the other end, the digital signal is converted back to an analog signal (your voice) so the person you are calling can hear you. The conversion at the other end allows you to speak to anyone with a regular phone number, whether they have VoIP service or regular phone service.   

No, you do not need a computer for phone-based VoIP services. An adapter (often provided free of charge by the VoIP provider) connects the phone to a high-speed internet connection. A computer can be helpful to utilize and manage different features offered by the provider; however, it is not needed.