They're going to be happy because their package is there at the house.
'They're' is the same as 'they are', so the sentence could be written as They are going to be happy because their package is there at the house. 'They're' is a contraction, much like could've for 'could have', didn't for ''did not, and so on.
'Their' is a possessive word. It means more than one person, at least two are involved in the possession of the noun in question. If only one person was involved in the possession of a noun, then the word used would be either 'his', 'her' or 'hers'. If the sentence had been about a man, it could have been written 'He'll be happy his package is there at the house.' You can change he'll to she'll and his to her if you wanted to write the sentence about a woman. It would read then like this: 'She'll be happy her package is there at the house.'
'There' is a location word. 'Here', another location word, is closer to the speaker or writer than 'there' is. 'There' shows that distance exists between the speaker or writer and the noun in question. Remember, 'there' and 'here' do not rhyme. 'There' rhymes with 'air', 'dare', 'bear' but 'here' rhymes with 'ear', 'gear', and 'mere.'
The sentence 'They're going to be happy because their package is there at the house.' shows that the people will be happy that the package belonging to them is at home.
