才 /cái/ has several important meanings.

Most often we use it in the sense ONLY THEN, NOT UNTIL. 

Basically the purpose of this word is to indicate that something is taking place LATER than we would wish. As in:

我晚上十点才有时间。/Wǒ wǎnshang shídiǎn cái yǒu shíjiān./ I DON’T HAVE TIME TILL 10pm.

Or in the sentence in the visual above..

才 is also part of words that have something to do with TALENTS, ABILITIES…