
loslassen
to let go
To stop physically holding on to something or someone.
Lass mein Handgelenk los, du tust mir weh!
Let go of my wrist; you're hurting me!
to let go / release
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to let go
To stop physically holding on to something or someone.
Lass mein Handgelenk los, du tust mir weh!
Let go of my wrist; you're hurting me!

to let go
To free yourself emotionally from a person, thought, or problem and no longer hold on to it.
Es ist schwer, die Vergangenheit loszulassen und nach vorne zu schauen.
It is hard to let go of the past and look ahead.

to release
To release an animal or a person so that it or they can move freely.
Der Hund wurde von der Leine losgelassen und rannte über die Wiese.
The dog was released from the leash and ran across the meadow.
'Loslassen' (to let go) is a separable verb. The prefix 'los' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Er ließ die Tasche einfach los.
He simply let go of the bag.
The verb is made up of the prefix 'los-' and the verb 'lassen' (to let). Here, 'los-' expresses separation or release, which gives the meaning 'to stop holding' or 'to free oneself'.
Bitte lass meine Hand los!
Please let go of my hand!
You can tell whether the physical or emotional meaning is intended from the object. With concrete things ('Hand' = hand, 'Seil' = rope), it is about holding on; with abstract terms ('Vergangenheit' = past, 'Sorgen' = worries), it is about emotional release.
Der Kletterer durfte das Seil auf keinen Fall loslassen.
The climber absolutely could not let go of the rope.
In a figurative sense, 'loslassen' (to let go) is often connected with emotional or abstract concepts. Typical phrases are: 'die Vergangenheit loslassen' (to let go of the past), 'die Kontrolle loslassen' (to let go of control), or 'alte Ängste loslassen' (to let go of old fears).
Im Urlaub konnte sie endlich den ganzen Stress loslassen.
On vacation, she was finally able to let go of all the stress.
to give up / submit
Here, Aufgeben means no longer pursuing a plan or goal. Loslassen, by contrast, emphasizes emotionally letting go of a hope or thought. So a goal may have been given up even though the emotional attachment has not yet been let go.

Nach der Trennung lässt Mia die Hoffnung auf eine Versöhnung langsam los.
After the breakup, Mia slowly lets go of her hope of reconciliation.
Nach der Trennung gibt Mia ihren Plan auf, Ben zurückzugewinnen.
After the breakup, Mia gives up her plan to win Ben back.