Packet switching is a communications paradigm in which packets (units of information carriage) are routed between nodes over data links shared with other traffic. In each network node, packets are queued or buffered, resulting in variable delay. This contrasts with the other principal paradigm, circuit switching, which sets up limited number of constant bit rate and constant delay connections between the nodes for their exclusive use for the duration of the communication.
When a unit of data, beginning at the application layer (top layer) is transmitted to lower layers, headers and trailers are appended to it. Once the unit of data reaches the IP layer and source and destination IP addresses are added to it, it then is known as an IP datagram. The unit of data, feeling a little bloated from having all this extra baggage is then sent to the link layer where source and destination MAC addresses are perpended to it. Now it is called a frame - and more accurately an Ethernet frame (if the physical layer is Ethernet). To be precise, the unit of data passed between the IP layer and the network interface card is really a packet of data. Thus, a packet can be an entire IP datagram or perhaps a fragment of an IP datagram.
UDP units of data, being connectionless (and thus not really too concerned whether the receiver actually got the data or not) are also referred to as datagrams.
This leaves octets. Octets are units of 8 bits (also know as bytes). Thus the maximum size of a frame in Ethernet is 1513 octets or 1513 bytes. Any larger and the frame must be split or fragmented. As you might expect, fragmentation causes delay so it is good to keep all your frames below the MTU size.