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Precognition is using spiritual power to know about things that will happen in the future.
Literal
Precognition [as-for-とは] spiritual-power [object-を] use, future [in-に] happen matters [about-について] knowing [thing-こと].
Another definitional sentence using ~とは to introduce the term. This is the encyclopedia/dictionary frame: '[term]とは[definition]こと.' The predicate ends in just こと (a bare nominalizer) without a copula — a slightly informal/abbreviated dictionary-entry register. ~について ('about X,' 'concerning X') is the standard phrase for 'about,' 'regarding' — here modifying 知る ('to know'). 未来に起こることがら ('matters that will happen in the future') is a relative clause with ことがら ('matters, affairs') as the modified noun. ことがら is a slightly formal/written noun for 'matter, topic, issue.'