Learn Turkish: Yarına kadar bekle.

The word kadar requires the word right before it to have the "to" or "towards" ending (the dative case). To say "until tomorrow", you must add the -a ending to yarın (tomorrow) to make yarına. You can think of the whole phrase as "up to tomorrow".

Does kadar always mean "until"?

Not always. On its own, kadar often means "as much as" or refers to an amount. However, when it follows a word that has the -a or -e direction ending, like in yarına kadar, the combination specifically means "until" a certain time or "as far as" a certain place.

Why does the verb bekle not have a tense ending like -iyor?

Because it is a direct command telling someone to "Wait!". In Turkish, to give a command to one person in an informal way, you simply take the dictionary form of the verb (beklemek, meaning "to wait") and drop the -mek or -mak ending. What is left is just bekle.