Engineering Definitions of Terms
"A" "B" "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M",
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Peak Surge Current. A fault current. An large abnormal increase in current flow. The maximum amount of current a component can handle for some short duration of time, with out failure.
This particular chart shows the Peak Surge Current for a Solid State Relay, rated at 2 amps [with a heat sink], or 1 amp with out the heat sink. The chart provides two curves, one for a relay with a heat sink and one with the component without a heat sink.

Peak Surge Current vs Surge Duration

Of course this graph is just one example of how a relay will handle surge current. The chart shows maximum surge current over time. That is, how long can a component withstand a particular amount of current.

Peak surge current relates to component heating, or over heating, which is why the graph provides curves for a heat sink. Note that the longer the duration of the over-current surge the smaller the amount of permissible surge current.

Peak Surge Current, or even just Surge Current is important when designing with a number of components, including relays. In fact it doesn't matter if the relay is solid state [semiconductor], or mechanical. A relay is one of those components that might be called upon to switch different types of loads, while many other components drive predictable loads. Because the load of a relay is undefined it's important to watch the maximum surge current.

Peak surge current may be applied to any component that draws current; however this graph only applies to one particular relay:
MIL-PRF-28750/9

Hermetically Sealed 400Hz, Optically Isolated Solid State Relay

A related topic covers How to Derate a Relay based on rated load and transient current surges. In this case a transient current is assumed greater than the rated current, or basically a surge current.