to leave someone, especially someone you are responsible for
what does "to" mean here?
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Dictionaries use the infinitive form both for the main word being defined and the words used to describe it.
is a "bare" infinitive (the to is omitted).
is a full 'to' infinitive. In a dictionary, it would be unhelpful for every verb to be preceded by "to", so it is omitted from the main word of each entry. But in full sentences forming a definition, it is added.
What does "to" mean? Nothing. It just marks the infinitive form in the same way that an inflection does in other languages (eg aimer in French or amare in Latin or Italian).