tragbar
portable
Light and small enough to be carried by one person.
Für die Reise habe ich mir einen tragbaren DVD-Player gekauft.
For the trip, I bought myself a portable DVD player.

portable / acceptable / wearable
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portable
Light and small enough to be carried by one person.
Für die Reise habe ich mir einen tragbaren DVD-Player gekauft.
For the trip, I bought myself a portable DVD player.

The word is made up of the verb stem 'trag-' (from 'tragen' (to carry/wear)) and the ending '-bar'. The ending '-bar' means that something can be done. So 'tragbar' (portable/wearable) literally means 'can be carried/worn'.
Dieser Koffer ist sehr leicht und daher gut tragbar.
This suitcase is very light and therefore easy to carry.
You can recognize the meaning of 'tragbar' (portable/acceptable/wearable) from the context. If it is about devices like a computer, it means 'portable'. With abstract things like costs or risks, it means 'acceptable'. In connection with fashion, it means 'wearable in everyday life'.
Ich suche einen kleinen, tragbaren Lautsprecher für den Urlaub.
I'm looking for a small, portable speaker for vacation.
In the meaning 'akzeptabel' (acceptable), 'tragbar' (acceptable) is often used with the preposition 'für' + accusative and a person or group. This expresses for whom a condition or risk is reasonable.
Die vorgeschlagene Lösung ist für alle Beteiligten tragbar.
The proposed solution is acceptable for everyone involved.
mobile
'mobil' and 'tragbar' can both mean that something can be used in different places. 'tragbar' says more specifically that something is small and light enough to carry. 'mobil' emphasizes more that something works on the go or in changing locations. With technology, the words can be close in meaning, for example with a 'mobiles Gerät' (mobile device) or a 'tragbares Gerät' (portable device). They can be confused because both refer to something that does not have to stay fixed in one place. As a practical rule: 'tragbar' is more about size and weight, while 'mobil' is more about use on the go.

Für die Reise nimmt Max einen tragbaren Lautsprecher mit.
Max is taking a portable speaker with him for the trip.
Mit dem mobilen Internet kann Anna auch im Zug ihre Nachrichten lesen.
With mobile internet, Anna can read her messages on the train too.