Both "об их" and "о их" are correct, but they are used in different contexts.

"Об их" is used when "их" is followed by a vowel sound, for example: об их детях, об их открытиях.

"О их" is used when "их" is followed by a consonant sound, for example: о их работе, о их правилах.

In both cases, "их" is a possessive pronoun meaning "their" in English.