Learn Turkish: Elinde bir elma var. - There is an apple in his hand.

Let's break down elinde: el (hand) + -i (his/her) + -n- (buffer letter) + -de (in). When you add a case suffix like -de (in/on/at) to a word that already has a 3rd-person possessive suffix like -i (his/her/its), Turkish requires the buffer letter -n- between them. You will see this -n- buffer a lot when talking about things belonging to "him", "her", or "it"!

I don't see the word for "his" (onun) in the sentence. How do we know it's his hand?

The possessive suffix -i attached to el already means "his" (or "her"). Because this suffix makes it perfectly clear whose hand it is, the pronoun onun is usually dropped. You would only add onun elinde if you wanted to emphasize that it is his hand and not someone else's.

Could elinde also mean "in your hand"?

Yes, it could! "Your hand" is elin (el + -in). If you add the location suffix -de to that, you also get elinde (in your hand). Because they look identical, you have to rely on context to know if it means "in his/her hand" or "in your hand".

Why does var come at the very end of the sentence?