Que is a connective word used in Spanish in subordinate clauses.
- When que is used in indirect speech, i.e reporting what someone says, we need to use "que": we cannot omit it, even though in English "that" is optional.
Here are some examples:
Luisa dice que va a llegar un poco tarde.Luisa says (that) she is going to be a bit late.
Mi padre me ha dicho que soy muy vanidoso.My dad told me (that) I am very vain.
Ella me dijo que su novio quería casarse con ella.She told me (that) her boyfriend wanted to marry her.
You can see in the examples above that you could omit "that" in English, but in Spanish you cannot omit "que"; the sentence would not make sense.
- When we use "que" as a relative pronoun, i.e referring to a noun, the same rule applies. Note that in this case, in English, you cannot always omit which/that either.
La vecina que vive en el tercer piso hace mucho ruido.The neighbour who lives on the third floor makes a lot of noise.
Nuestro perro, que tiene solo 3 meses, tuvo un accidente ayer.Our dog, who is just 3 months old, had an accident yesterday.
El chocolate que te comiste era mío.The chocolate (that) you ate was mine.
These sentences would be incorrect in Spanish, they don't make sense without que:
El chocolate te comiste era mío.
Nuestro perro, tiene solo 3 meses, tuvo un accidente ayer.
Luisa dice que va a llegar un poco tarde.Luisa says (that) she is going to be a bit late. Mi padre me ha dicho que soy muy vanidoso.My dad told me (that) I am very vain. El chocolate que te comiste era mío.The chocolate (that) you ate was mine. Nuestro perro, que tiene solo 3 meses, tuvo un accidente ayer.Our dog, who is just 3 months old, had an accident yesterday. La vecina que vive en el tercer piso hace mucho ruido.The neighbour who lives on the third floor makes a lot of noise. Ella me dijo que su novio quería casarse con ella.She told me (that) her boyfriend wanted to marry her. 
