verheiratet sein
to be married
To be in the state of having entered into marriage; not to be single, divorced, or widowed.
Meine Eltern sind seit über 30 Jahren glücklich verheiratet.
My parents have been happily married for over 30 years.

to marry / to marry off
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to be married
To be in the state of having entered into marriage; not to be single, divorced, or widowed.
Meine Eltern sind seit über 30 Jahren glücklich verheiratet.
My parents have been happily married for over 30 years.

The prefix 'ver-' is inseparable and often signals a change of state. Here it describes the transition into the state of marriage. So the verb is not separated.
Die Eltern verheirateten ihre Tochter aus politischen Gründen.
The parents married off their daughter for political reasons.
The use of 'verheiraten' changes with the grammar: 'verheiratet sein' (to be married) describes the state, 'jemanden verheiraten' (to marry someone off) describes the action by a third person, and 'sich verheiraten' (to get married) is a reflexive form for one's own marriage.
Sie ist seit fünf Jahren verheiratet.
She has been married for five years.
If you want to say whom someone is married to, you use the preposition 'mit' (with) followed by the dative.
Er ist mit seiner Jugendliebe verheiratet.
He is married to his childhood sweetheart.
The form 'jemanden verheiraten' (to marry someone off) is often used when a third party (e.g., the parents) arranges a marriage for someone else. It often has a historical or traditional undertone.
In vielen alten Geschichten werden die Prinzessinnen gegen ihren Willen verheiratet.
In many old stories, the princesses are married off against their will.
to marry
'sich verheiraten' and 'heiraten' can both mean that two people get married. In normal everyday language, 'heiraten' is much more common and sounds more natural. 'sich verheiraten' is also understood, but it sounds a bit more formal or less modern. The words can be confused because both fit the idea of entering into marriage. The form is important: people usually say 'Anna heiratet Max' or 'Anna und Max heiraten'. 'Anna verheiratet sich mit Max' is possible, but less common.

Sie hat sich vor zwei Jahren mit ihrem Freund verheiratet.
She married her boyfriend two years ago.
Nächsten Sommer heiratet er seine Partnerin im kleinen Kreis.
Next summer, he is marrying his partner in a small private ceremony.