There is a difference between Their and They're. While "their" means belonging to them, they're is a contraction which stands for "they are".
Comparison chart
 | Their | They're |
|---|---|---|
| Used as a contraction | No | Yes - they're is an abbreviation for "they are" |
| Meaning | Belonging to them | They are |
Examples
- She was envious of their expensive shoes.
- It's time to go. They're here to pick us up.
- They're claiming to do everything they can to clean up the oil spill.
- Workers' unions in France are protesting the change in their retirement age from 60 to 62.
Video explaining the differences
The following video explains the differences between "there", "their" and "they're".
Double Quotes 
Their 
There 
You're 
It's
Comments: Their vs They're