I would like someone to explain when and how these two word are used?
Hi, these words sound the same but they mean very different things. The word ‘there’ is a word that points to a place. ‘Their’ means that something belongs to a group of people. ‘Their’ is also used instead of his or hers as a generic pronoun. Please read the example below about food cooking over charcoal. In that sentence, the word ‘their’ is used as a generic pronoun. It is used as a substitute for his and/or hers. I guess the problem is that the gender of the person cannot be known without more specific information about the neighbour. Does that make sense? I think it’s also possible to use the word ‘your’ rather than ‘their’ as a generic pronoun.
I used a free website called
for information about this question. It’s very easy to use. Sorry if this answer is too long but I’ve taken care to read about it because it’s a little bit tricky.

1 there
Function: adverb
There used in a few sentences
(a) Stand over there until I call you.
(b) Put it there on that table
(c) Please go home and stay there.
A word with the opposite meaning: here
(a) in or at that place
(b) in or at a place other than that of the speaker -- opposed to here

2 their
Function: adjective. It is Used as a modifier before a noun: their accomplishments; their home town.
Their used in a sentence: the delicious aroma drifting across a neighbour's fence of food cooking over charcoal is enough to make anyone yearn for a barbecue of their own.
Definition: the possessive form of