A packet in telephony refers to the mechanism of packet switching for transporting voice or data as opposed to the more traditional mechanism of circuit switching. In VoIP, which is voice over IP, it refers directly to the way the IP frames of data are packaged into deliverable packets with a source and destination address assigned to each one.
IP packets are how the VoIP data can be delivered from one network connected device to another across interconnecting networks. IP packets are more efficient with regards bandwidth as they carry variable sized payloads. For example, during a Telnet session an IP packet may only contain a single alphanumeric character or symbol. On the other hand, a huge FTP file of many tens of megabytes can also be catered for by splitting the file many 1500-byte segments and reconstructing the stream of packets upon delivery. This is in contrast to circuit-based technology that is of a fixed cell size and requires padding to fill up any unused space; this is a waste of bandwidth, though it is very accurate and predictable about timing.
The internet uses packets to send data to destinations via a collection of routers that can determine the best path to the destination through routing tables. These routing tables are local maps of the internet from the perspective of that specific router. By routing IP packets in this way, any destination on the internet can be quickly found on a hop-to-hop basis without the need for preconfigured circuits.
IP packets travel independently of other packets even within their own data streams so an important feature of IP is that it can prioritize individual packets to give latency-sensitive voice and video data packets within a stream precedence over non-urgent data.