Anything on the path between the endpoints that looks at layers above IP. Obvious examples are NATs, firewalls, transparent proxies, traffic normalizers, so-called protocol accelerators. Some boxes I've no idea what they do. Take a look at our paper in reference [0] above, which probes what they actually do to traffic.
Middleboxes are machines somewhere along the path (when you're sending to a particular destination) that drop, filter, bandwidth shape, or otherwise edit your traffic. Basically anything besides packet forwarding.
Middlebox is a technically imprecise term that is not in common usage among technical people anywhere. Why people in this thread are trotting it out is anyone's guess.
Middlebox has quite precise technical meaning: anything that works at higher layer than on which it is visible to neighboring network.
Usualy this refers to various "security" "solutions" which attempt to do deep packet inspection and generally break various things, but it also can mean NAT or L2 bridges that do filtering on L3/L4 headers (for example DOCSIS CMs and CMTSes are such middleboxes)
That's just plain wrong, in the context of protocol development it is a commonly used term, and not exactly uncommon in wider networking space as well. See MPTCP mentions in this thread, presentations and mailing lists around development of TLS, HTTP2, QUIC, ...
