* Referring to a plural noun: "The students left their books on the table."
* Referring to a singular noun with a collective identity: "The team celebrated their victory." (This is a common and increasingly accepted usage, even though grammatically it's plural referring to a singular entity.)
* Referring to a singular, unspecified gender: "Everyone should bring their own lunch." (This is a common and accepted use, despite the singular antecedent.)
The key is that "their" is a possessive pronoun showing ownership or belonging and always refers to a plural noun or a group of people. Avoid using it with a singular noun of known gender unless you want to use an inclusive, gender-neutral approach.