aufheben
to pick up
To pick something up from the floor or from a lower position with your hands.
Er bückte sich, um den heruntergefallenen Schlüssel aufzuheben.
He bent down to pick up the key that had fallen.

to pick up / keep / cancel
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to pick up
To pick something up from the floor or from a lower position with your hands.
Er bückte sich, um den heruntergefallenen Schlüssel aufzuheben.
He bent down to pick up the key that had fallen.

'Aufheben' is a separable verb. In a main clause, the prefix 'auf' goes at the end of the sentence. In subordinate clauses or in the infinitive with 'zu', the verb is not separated.
Sie hebt den Stift vom Boden auf.
She picks the pen up from the floor.
The verb consists of 'auf' and 'heben' (to lift). The literal meaning 'hochheben' (to lift up) (meaning 1) is the basis for the other, more abstract meanings: you 'hebst' something 'auf' in order to keep it, or you 'hebst' a rule 'auf' in order to make it invalid.
Kannst du bitte das Buch aufheben?
Can you please pick up the book?
You can recognize this meaning by the fact that it is always about a concrete, physical object that is in a lower place (e.g. on the floor, on the table).
Er hat die Münze aufgehoben, die ihm aus der Tasche gefallen war.
He picked up the coin that had fallen out of his pocket.
In the meaning 'aufbewahren' (to keep/store), the verb is often combined with things that have personal or practical value. Typical examples are: 'den Kassenbon aufheben' (to keep the receipt), 'alte Briefe aufheben' (to keep old letters), 'eine Erinnerung aufheben' (to keep a memory/memento).
Heb den Kassenbon gut auf, falls du das Gerät umtauschen musst.
Keep the receipt safe in case you need to exchange the device.
This meaning is almost always used in an official, legal, or administrative context. The object is typically something abstract, such as a law, a judgment, a ban, or a contract.
Wegen des Sturms wurden alle Flüge für heute aufgehoben.
Because of the storm, all flights for today were canceled.
The reflexive form 'sich aufheben' means that two opposing things balance each other out. The subject is always plural or refers to a set of things.
Die beiden Kräfte sind gleich stark und heben sich daher gegenseitig auf.
The two forces are equally strong and therefore cancel each other out.
The expression 'sich gut/sicher/wohl aufgehoben fühlen' (to feel well/safely/comfortably looked after) is a fixed unit. It describes the feeling of being well cared for and safe in a place or with people.
In diesem Team fühle ich mich von Anfang an gut aufgehoben.
I have felt well looked after in this team from the very beginning.
to record / take in
'aufnehmen' and 'aufheben' can both have to do with something not simply staying where it is or getting lost. But the difference is important: 'aufnehmen' here means that something goes into something, for example water into a sponge or information into your head. 'aufheben' is used when you pick something up from the floor or keep something for later. The words can be confused because both begin with 'auf-' and, in some situations, are connected with an upward movement. If you take something from the floor, it is normally 'aufheben'; if something goes into a body, a material, or a system, 'aufnehmen' fits.

Mein Nachbar hebt den Schlüssel vom Boden auf.
My neighbor picks the key up from the floor.
Der Schwamm nimmt das Wasser schnell auf.
The sponge absorbs the water quickly.