herausholen
to take out
To remove something or someone from a place, container, or situation, or to bring it outside.
Sie holte einen alten Brief aus der Schublade heraus.
She took an old letter out of the drawer.

to take out / get out
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to take out
To remove something or someone from a place, container, or situation, or to bring it outside.
Sie holte einen alten Brief aus der Schublade heraus.
She took an old letter out of the drawer.

'Herausholen' (to take out / get out) is a separable verb. The prefix 'heraus' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Er holt ein altes Fotoalbum heraus.
He takes out an old photo album.
The prefix 'heraus' combines 'her' (movement toward the speaker) and 'aus' (out of something). So the verb describes taking something from inside to outside, in the direction of the speaker.
Kannst du mir bitte die Milch aus dem Kühlschrank herausholen?
Could you please take the milk out of the fridge for me?
In the literal meaning, the preposition 'aus' with the dative is almost always used to name the place from which something is removed. The structure is: etwas (accusative) aus etwas (dative) herausholen.
Die Feuerwehr holte den Fahrer aus dem Auto heraus.
The fire department took the driver out of the car.
When the idea is maximizing performance, 'herausholen' (to get out) is often combined with abstract nouns like 'das Beste' (the best), 'das Maximum' (the maximum), or 'alles' (everything). The source is often a person or a situation.
Der Trainer will das Beste aus der Mannschaft herausholen.
The coach wants to get the best out of the team.
In this meaning, it is about getting information from a person, often against that person's will. Typical objects are 'ein Geständnis' (a confession), 'die Wahrheit' (the truth), or 'Informationen' (information).
Der Detektiv versuchte, die Wahrheit aus dem Zeugen herauszuholen.
The detective tried to get the truth out of the witness.
to remove
'entfernen' and 'herausholen' can both mean that something is moved away from a place. 'entfernen' mainly emphasizes that something is gone or removed. 'herausholen' emphasizes the movement from inside to outside, for example out of a bag, a cupboard, or a difficult situation. When the place or container is important, 'herausholen' sounds more natural. When the only important point is that something should be gone, 'entfernen' fits better.

Meine Mutter holt die warmen Decken aus dem Schrank heraus.
My mother takes the warm blankets out of the cupboard.
Ihr entfernt die kaputten Teile, bevor ihr das Regal wieder aufbaut.
You remove the broken parts before putting the shelf back together.