Learn Swedish: Meditationen kräver såväl kroppslig som mental närvaro. - Meditation demands both physical and mental presence.

They both mean "both ... and", but såväl ... som is more formal. You will often see it in written text, journalism, or professional instructions, while både ... och is the standard choice for everyday conversation.

Why is the definite form meditationen used here when the English translation just says "Meditation"?

When talking about an abstract concept, a discipline, or a general phenomenon, Swedish frequently uses the definite form. You have likely seen this rule before with words like livet (life) or kärleken (love).

Why are the adjectives kroppslig and mental in their base forms? Shouldn't they take plural endings since there are two traits mentioned?

No, because they both describe the same singular en-word: en närvaro (a presence). Even though they are joined by the conjunction såväl ... som, they individually modify the singular noun, so they both take the base en-word form without an added -a.

What is the difference between kroppslig and fysisk? Could I use fysisk here?

Yes, fysisk would also work. However, kroppslig comes directly from the noun kropp (body), so it translates more closely to "bodily". It creates a very clear and natural contrast with mental (of the mind) in this specific context.