
pennen
to sleep
Colloquial expression for sleeping.
Ich bin total müde, ich geh jetzt pennen.
I'm totally tired; I'm going to sleep now.
to sleep / to space out
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to sleep
Colloquial expression for sleeping.
Ich bin total müde, ich geh jetzt pennen.
I'm totally tired; I'm going to sleep now.

to space out
Colloquial for being inattentive or missing something important. It is often used in the past participle ('gepennt haben').
Da habe ich wohl kurz gepennt und die richtige Ausfahrt verpasst.
I must have spaced out for a moment and missed the right exit.
'Pennen' (to sleep / to space out) is a very informal, colloquial word. Use it only with friends or in casual situations, but not in formal emails or at work.
Sorry, ich kann heute Abend nicht, ich will nur noch pennen.
Sorry, I can't tonight; I just want to sleep.
In the meaning 'schlafen' (to sleep), 'pennen' is often used with 'bei jemandem pennen' (to sleep over at someone's place) or 'tief und fest pennen' (to sleep very soundly).
Nach der Party kann ich bei einem Freund pennen.
After the party, I can sleep over at a friend's place.
In the meaning 'unaufmerksam sein' (to be inattentive), the fixed expression '(da) habe ich gepennt' (I spaced out there) is almost always used in the perfect tense. It expresses that you made a mistake or missed something important.
Ich habe die Ankündigung nicht gehört, da habe ich wohl gepennt.
I didn't hear the announcement; I must have spaced out.
to sleep
Schlafen and pennen can refer to the same state of sleep. Schlafen is neutral and suitable in almost any situation; pennen is distinctly colloquial and is mainly used in casual conversations.

Der Junge sagt seinem Freund, dass er seit Tagen schlecht pennt.
The boy tells his friend that he has been sleeping poorly for days.
Die Mutter sagt dem Arzt, dass ihr Sohn seit Tagen schlecht schläft.
The mother tells the doctor that her son has been sleeping poorly for days.