Homonyms are words that sound the same, but are spelled differently and have different meanings and usages. This can be confusing sometimes as one must rely on context to figure out which word is meant or should be used. 

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Even native speakers sometimes fail to use the homonyms "there," "their," and "they're" correctly. Here is a quick review of which one is appropriate for which occasion. 

1) The word "there" is used to refer to a physical or abstract location.

When I flew in on the float plane, they were all there on the boat.

When I flew in on the float plane, they were all there on the boat.

Caption 4, Alaska Revealed - Endless Wave

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Also, it is commonly combined with a conjugation of “to be” or a modal verb to discuss the existence of something.

For everywhere we look, there is work to be done.

For everywhere we look, there is work to be done.

Caption 28, Barack Obama's Inauguration Day - Obama's Speech

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I think there must be something wrong with me, Linus.

I think there must be something wrong with me, Linus.

Caption 9, A Charlie Brown Christmas - Opening

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2) "Their" is a possessive adjective used before a noun when the subject is "they." With "their," we are speaking about something that belongs to two or more people.

What are their names? -Their names are Naya and Alex.

What are their names? -Their names are Naya and Alex.

Caption 14, Caralie and Annie - Get to Know Each Other

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Their goal is a plan to finally help humanity reduce its carbon footprint.

Their goal is a plan to finally help humanity reduce its carbon footprint.

Caption 3, Green TV - What Is COP21?

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3) "They’re" is a contraction of "they are" used to refer to two or more people in the third person. It is especially useful for shortening sentences in the present continuous tense.

I think they're nice.

I think they're nice.

Caption 12, Comic-Con 2015 - Jennifer Lawrence

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They're playing a game on the lawn.

They're playing a game on the lawn.

Caption 10, Jessica - in Prospect Park

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Further Learning
Check out the examples above on Yabla English to get a better sense of the full context for the use of "there," "their," and "they're." Try to write a few sentences in which you use two or even all three of these words to solidify your understanding. An example would be: "They're not sure when they will get there. It depends on when their plane lands."