To be reactive is to be ready to react or respond to something else — as opposed to ready to act on one's own. A person who's reactive does things only in response to others.

To react is to do something in response to something else. When someone pinches you, for example, you react. But if you're a reactive person, then you only react; you're always ready to react but not to act on your own. You're rather lifeless unless something or someone else causes you to do act. This is usually seen as a negative trait in people, unless you're talking about, say, firefighters or cops. We admire people who don't need prodding to get things done. Some chemicals are called reactive, too, because they react readily with other chemicals.

Definitions of reactive
  1. adjective
    participating readily in reactions
    “sodium is a reactive metal”
    “free radicals are very reactive
    activated, excited
    (of e.g. a molecule) made reactive or more reactive
    (chemistry, physics, biology) readily undergoing change or breakdown
    capable of undergoing a chemical reaction with oxygen
    (chemistry, physics, biology) readily changed or destroyed by heat
    highly or violently reactive
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    (chemistry) not reacting chemically
    (chemistry) not participating in a chemical reaction; chemically inert
    indifferent, inert, neutral
    having only a limited ability to react chemically; chemically inactive
    inert especially toward oxygen
    not taking part readily in chemical change
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  2. adjective
    reacting to a stimulus
    “the skin of old persons is less reactive than that of younger persons”
    synonyms: responsive
    responsive to physical stimuli
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