Reactions. Certain special abilities, spells, and situations allow you to take a special action called a reaction. A reaction is an instant response to a triggering event. The triggering event and what you can do in response to it are defined by the thing that allows you to take a reaction.
The triggering event can occur on your turn or on someone else’s. It is possible, then, to take a reaction before your first turn in combat. See here.
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If you’re surprised, you can’t take a reaction until your first turn ends. Thus, if you have a high initiative result and your turn is over, you can take a reaction during the remainder of the first round.
When can you take another reaction? See here.
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The opportunity attack is a common and important reaction.
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An action or move taken via the Ready action is considered a reaction.
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Certain class features allow you to do a certain thing as a reaction in response to a particular situation. See, for example, the Uncanny Dodge class feature of a rogue.
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Some magic items enable you to take a reaction in response to certain situations. An arrow-catching shield is an example.