Circle of death
Circle of death is a strange, archaic term, and frequently used term for the common tournament occurrence of "a three-way tie." It is a typically used to refer to such a tie when it affects either overall placement or which teams make the playoffs, as it necessitates a more-complicated-than-usual tiebreaking procedure.
It is also possible to get a five-way tie, where everyone is 2-2 among the tied teams.
Resolving a circle of death
In general, it is not necessary to split a tie - most tournaments leave every place other than first unresolved. The gold standard is to have the two lagging teams play for the opportunity to play the leading team. This can be done on whole or (more commonly) half packets.
It is considered "good quizbowl" to avoid paper tiebreakers like head-to-head, PPG, or bonus conversion when possible, though they are used when time or the number of questions is limited. The current ACF rules provide for the use of PPG and then bonus conversion if there are not enough packets to play off the tie.
Other uses
The term "circle of death" is also used by the NAC to designate the double-elimination playoff at the end of the tournament.