Level and edge-triggering are two main types of sensitivities of circuits or components to a gating signal, such as a clock.
Level-Triggered
A level-triggered or level sensitive circuit or component can change its output as long as a gating signal, such as a clock signal, is on.
Latches are an example of level sensitive devices.
Edge-Triggered
An edge-triggered or edge sensitive circuit or component can change its output only during clock pulse transition. It is notated in circuit diagrams by using a triangle symbol.

Edge-triggered circuits or components are either positive-edge triggered or negative-edge triggered depending on whether they change their output on a rising or falling clock edge.
Flip-flops are examples of edge sensitive devices.
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