The number of phages produced per infected bacterium or on average across of a population of phage infections.
The concept of burst size in a literal sense is limited to describing lytic infections, where "burst" refers to the lysis event. As noted, burst sizes can be determined as population averages (average burst size) or, less frequently and requiring substantially more work, on a per-infection basis (single-burst experiment). Usually when people refer to burst size they are referring to the average burst size, though occasionally this is not the case.
Determination of burst size involves comparing infective centers found in cultures prior to phage-induced bacterial lysis versus infective centers present in cultures following such lysis. Effort also should be made to assure that only a single round of infection occurs (no post-lysis infection prior to enumeration) as well as that no more than approximately one phage infects each infected bacterium.
This is the definition from Adams (1959), p. 439, for simply "Burst": "Yield of phage liberated by spontaneous lysis of an infected bacterium. This may be measured directly for isolated bacteria in single burst experiments, or as an average burst size in one-step growth experiments. Also the act of liberation."
For further consideration especially of means of burst-size determination, see Hyman and Abedon (2009).
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