I have just learned German. I have heard a lot of people say the word "da" in conversation, but I don't know what it means. And dictionary doesn't help. Can somebody help me translate this word and give me some examples how to use it correctly.
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Da is either a conjunction connecting the main clause with a causal clause or it is an adverb.
As a conjunction Duden defines three different usages one of which is archaic. The other two usages are quite common. First it has the meaning of because, since as in
The second usage as conjunction includes a temporal meaning.
As an adverb there are several different usages including spatial and temporal location:
There are (= Da sind) more than those mentioned usages. For example da is also used in meaning of in this respect. More examples and usages are listed on Duden.
In addition to the above, 'da' is also used with prepositions to 'step in' for the noun (a bit like a pronoun). A preposition requires a noun, as in example 1 below. We can replace 'vor dem Hund' with 'davor' if it is obvious what we are referring to, as in example 2. It can also refer to entire clauses, as in example 3.
1) Ich habe Angst vor dem Hund.
2) Ich habe Angst davor.
3) Ich habe Angst davor, dass mich der Hund beißt.
This works with many prepositions. (Sometimes you add an extra 'r' to prevent two vowels coming together).
*) Er kümmert sich um das Kind. Er kümmert sich darum. Er kümmert sich darum, dass das Kind zur Schule kommt.
*) Du hast dich mit dem Messer geschnitten. Du hast dich damit geschnitten.
*) Wir wissen alles über Mathe. Wir wissen alles darüber.
In addition to what others explained, da before all means there. And just like in English, it's often used as fillword. That might the reason why you hear people say it in conversations rather frequently, e.g.
There are two meanings of da
I would translate it as "Since I'm here, I'm here."