drauf
on it
Colloquial short form of 'darauf' (on it); refers to a position on something.
Stell die Tasse nicht auf den Tisch, der Deckel ist noch drauf.
Don't put the cup on the table; the lid is still on it.

on it / feeling / high
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on it
Colloquial short form of 'darauf' (on it); refers to a position on something.
Stell die Tasse nicht auf den Tisch, der Deckel ist noch drauf.
Don't put the cup on the table; the lid is still on it.

'Drauf' is a word from spoken language. In formal situations or in written texts such as emails to strangers or essays, you should avoid it.
Leg das Buch einfach oben drauf.
Just put the book on top.
'Drauf' is the colloquial short form of the pronominal adverb 'darauf' (on it). It refers to a thing or a surface that was mentioned before.
Hier ist der Tisch. Stell die Vase bitte drauf.
Here is the table. Please put the vase on it.
A person's mood is described with the fixed expression '[adverb] drauf sein' (to be in a [adverb] mood/state). Typical adverbs are 'gut' (good), 'schlecht' (bad), or 'komisch' (strange).
Warum bist du heute so schlecht drauf?
Why are you in such a bad mood today?
The expression 'etwas drauf haben' means that someone is very talented or competent. The verb in this expression is always 'haben' (to have).
Sie hat in Mathematik wirklich was drauf.
She is really good at math.
The phrase 'den Tag drauf' is a fixed expression and means 'am folgenden Tag' (on the following day). It is used as a time expression in the sentence.
Am Freitag war die Party, und den Tag drauf war ich total müde.
The party was on Friday, and the day after I was totally tired.
In this meaning, 'drauf sein' is a slang expression. It is used to describe that someone is under the influence of drugs.
Man konnte sich nicht mit ihm unterhalten, er war völlig drauf.
You couldn't have a conversation with him; he was completely high.
afterward / after that
'danach' and 'drauf' can both refer to a time after an event. In this sense, 'am Tag drauf' means roughly 'am Tag danach' (the day after). The important difference is style: 'danach' is neutral and almost always fits, including in writing. 'drauf' is colloquial and, in this meaning, is mainly used in fixed expressions like 'am Tag drauf' (the day after). Learners may confuse the words because 'drauf' is often short for 'darauf', but it cannot replace 'danach' everywhere. If you are unsure, 'danach' is the safe choice.

Am Tag drauf hat Max sich für die Hilfe bedankt.
The day after, Max thanked them for their help.
Wir waren erst im Kino und sind danach noch etwas essen gegangen.
We went to the movies first and then went out for something to eat afterward.