A connector (or conjunction) is a grammatical word that joins to sentences:
- Do you like tea? + Do you prefer coffee? = Do you like tea or do you prefer coffee?
- I'm late + the bus was late = I'm late because the bus was late.

AND
This connector joins two sentences to make a new sentence where both sentences are true:
- John is a doctor and Mary is a nurse

OR
This connector joins two sentences to make a new sentence where only one is true:
- He lives in Rome or he lives in Paris, I can't remember

BUT
The first sentence is true but the second sentence expresses a difficulty:
- I like her, but I don't want to marry her
- China is very far away, but we can take the plain

BECAUSE
The second sentence explains the reason why the first sentence is true:
- I don't want to dance with you because I'm very tired.
In conversation, we can use the colloquial variation: 'CAUSE
- I can't go to the cinema 'cause I haven't got any money

SO
The second sentence is the consequence of the first sentence:
- It was very late in the evening, so we went to bed (= We went to bed because it was very late)
- She wanted to see me so I went to her house (= I went to her house because she wanted to see me)
- My train is leaving so I must go (= I must go because my train is leaving)

WHEN
The second sentence expresses the time when the first sentence happened:
- She opened the door when I arrived
- I don't like going to the sea when it's cold

IF
The sentence with IF expresses a condition. When the condition is true, the other sentence is true too:
- I'll go to your house if you need me
- If it is too hot, this light turns red

THAT
Very often we can see in English two sentences together with no connector:
- I know you love me.
1- I know. + 2- You love me. = I know that you love me = I know you love me.

In these cases, the connector is THAT, but this connector disappears most of the times, especially when talking. +Don't confuse this connector "that" with the demonstrative "that":
- I know that you love me connector
- I know that, you don't need to tell me demonstrative
This connector doesn't mean anything, it simply marks that a sentence is part of a bigger sentence, just like a noun or an adjective can. We can also use this connector to make relative clauses.

RELATIVE CLAUSES
We can explain or extend the meaning of a word by adding a "relative clause". That word is called "the antecedent".
The book is on the table + You want the book = The book that you want is on the table
In this sentence the antecedent is BOOK, and the sentence "that you want" gives information about the book.

Relative clauses use different connectors depending on the antecedent:
Person that / who
The man is Pete + The man speaks French = The man that speaks French is Pete = The man who speaks French is Pete.
Thing that/which
The book is a dictionary + You need the book = The book that you need is a dictionary = The book which you need is a dictionary

In some sentences (not always), the connector THAT can disappear:
- The woman that you love is very nice = The woman you love is very nice.
 
You don't need more details now, you only need a general idea of the connectors and relative clauses. But if you want more information about how connectors behave, you can read this:

The Compound Sentence: Connectors