einpacken
to pack
To put objects into a container such as a suitcase, bag, or box in order to transport or store them.
Ich muss noch meinen Koffer für die Reise einpacken.
I still have to pack my suitcase for the trip.

to pack / wrap
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to pack
To put objects into a container such as a suitcase, bag, or box in order to transport or store them.
Ich muss noch meinen Koffer für die Reise einpacken.
I still have to pack my suitcase for the trip.

'Einpacken' (to pack / wrap) is a separable verb. The prefix 'ein-' comes at the end in a main clause. In subordinate clauses or in the infinitive with 'zu', the verb stays together.
Ich packe schnell noch ein paar Bücher ein.
I'll quickly pack a few more books.
The reflexive form 'sich einpacken' (to bundle up) means to dress very warmly. It is often used as a command in the imperative.
Pack dich gut ein, es sind minus zehn Grad draußen!
Bundle up well; it's minus ten degrees outside!
The meaning 'aufgeben' (to give up) or 'eine Niederlage akzeptieren' (to accept defeat) is colloquial. It is mostly used in informal situations, often in sports or competitions.
Nachdem er zum fünften Mal verloren hatte, meinte er: „Okay, für heute kann ich einpacken.“
After he had lost for the fifth time, he said, 'Okay, I can pack it in for today.'
When it comes to traveling, 'einpacken' (to pack) is often combined with the objects or the container. Typical phrases are: 'den Koffer einpacken' (to pack the suitcase), 'die Badesachen einpacken' (to pack swimwear), or 'Proviant einpacken' (to pack provisions).
Hast du auch Sonnencreme und einen Hut eingepackt?
Did you also pack sunscreen and a hat?
This meaning is often used in the context of gifts or purchases. A typical question in a store is: 'Soll ich es Ihnen als Geschenk einpacken?' (Shall I wrap it for you as a gift?).
Sie hat das Geburtstagsgeschenk in buntes Papier eingepackt.
She wrapped the birthday present in colorful paper.
to take along / take away
'mitnehmen' and 'einpacken' can both come up in the context of trips, outings, or appointments. 'einpacken' describes the step before: you put something into a bag, suitcase, or box. 'mitnehmen' describes that you then have the thing with you and bring it to another place. That is why you can pack something but forget it at home and not take it along. Learners confuse the words because both are often connected with luggage. Practically speaking: first you pack something, then you take it with you.

Vor der Reise packt Lisa ihre warmen Pullover in den Koffer ein.
Before the trip, Lisa packs her warm sweaters into the suitcase.
Nimm am Wochenende genug Medikamente mit.
Take enough medication with you this weekend.