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A linking particle, γάρ marks a clause which is an explanation or an example of what's gone before. As with all particles, it is dangerous to learn a single word to translate it with. The best translation will depend on a variety of factors, including the register of the speech. You need to consider both the γἀρ sentence and the preceding sentence to work out the link.
You may have learnt that γάρ means ‘for’, but this really only tells part of the story. We can certainly say that in some instances, γάρ marks an explanation of the previous proposition. In current English, ‘for’ is used in formal registers with the same sense:
Starting today, we must pick ourselves up, dust ourselves off, and begin again the work of remaking America. For everywhere we look, there is work to be done. (Barack Obama, Inaugural Address, Jan 20, 2009)
So ‘for’ is a possible translation of γάρ in the right context. For example:
καὶ τοὺς ἀκούοντας οὐ χαλεπῶς ἔπειθον· ἀποκτιννύναι μὲν γὰρ ἀνθρώπους περὶ οὐδενὸς ἡγοῦντο, λαμβάνειν δὲ χρήματα περὶ πολλοῦ ἐποιοῦντο.
They had no difficulty in persuading their audience. For they thought little of killing people, but put high store in making money.
Lysias Speeches 12.7
In the formal legal context of this example, ‘for’ is not out of place.
However, to my ears at least, ‘for’ sounds out of place in less formal registers, for example in spoken dialogue. In these cases, ‘because’ can be more suitable. For example:
“νέοι ἐστέ,” εἰπεῖν, “τὰς ψυχὰς πάντες· οὐδεμίαν γὰρ ἐν αὐταῖς ἔχετε δι’ ἀρχαίαν ἀκοὴν παλαιὰν δόξαν οὐδὲ μάθημα χρόνῳ πολιὸν οὐδέν.
"You are all young in your souls," he said "because you have no opinion that is hoary with age, nor any understanding grey with time".
Plato Timaeus 224b
However, choosing the best translation of γάρ is not a simple choice between ‘for’ or ‘because’ depending on register. For example:
νήπιός εἰς, ὦ ξεῖν', ἢ τηλόθεν εἰλήλουθας,
ὅς με θεοὺς κέλεαι ἢ δειδίμεν ἢ ἀλέασθαι·
οὐ γὰρ Κύκλωπες Διὸς αἰγιόχου ἀλέγουσιν
οὐδὲ θεῶν μακάρων, ἐπεὶ ἦ πολὺ φέρτεροί εἰμεν·
Stranger, you're a fool, or else you aren't from round here
as you tell me to fear or avoid the gods.
We Cyclopes don't worry about aegis-bearing Zeus
or the blessed gods - we are better than them by far.
Homer Odyssey 9.273
In these sentences the γάρ is explaining why the Cyclops has called Odysseus a fool. It is therefore linking back to the previous main clause rather than the clause that immediately precedes it.
This sense can get lost in a bad translation. For example, in the following translation it is not clear what the ‘for’ is ‘for’-ing:
You are a fool or have come from afar who orders me to fear or avoid the gods. For the Cyclopes don't worry about Zeus...
In other instances, the γάρ is explaining something implicit rather than explicit in the text. This happens frequently in dialogue:
Σωκράτης: ἀλλά μοι πειρῶ πρᾴως τε καὶ εὐκόλως ἀποκρίνεσθαι.
Ἱππίας: αἰσχρὸν γὰρ ἂν εἴη, ὦ Σώκρατες, εἰ ἄλλους μὲν αὐτὰ ταῦτα παιδεύω καὶ ἀξιῶ διὰ ταῦτα χρήματα λαμβάνειν, αὐτὸς δὲ ὑπὸ σοῦ ἐρωτώμενος μὴ συγγνώμην τ’ ἔχοιμι καὶ πρᾴως ἀποκρινοίμην.
Socrates: Try to answer me nice and kindly.
Hippias: It would be terrible if I didn't try to understand you and answer your questions nicely when I teach these topics to others and consider my services worthy of payment.
Plato Hippias Minor 364d
Here, the γάρ is explaining why Hippias is agreeing to Socrates’ request, although there are no actual words saying that he is agreeing! We might make the agreement explicit in a translation to make the sense clearer:
S: Try to answer me nicely.
H: Alright, I will - after all, it would be pretty bad if…
In all the previous instances, γάρ has been giving an explanation, marking some kind of causal link between two ideas. However, there are other instances where there is no causal link between the previous sentence and the γάρ sentence. Instead γάρ serves to exemplify rather than to explain and therefore may not be translated ‘because’. For example:
τοιαῦτα λέγοντες οὐ τοιαῦτα ποιεῖν ἐτόλμων, ὡς ἐγὼ περὶ τῶν ἐμαυτοῦ πρῶτον εἰπὼν καὶ περὶ τῶν ὑμετέρων ἀναμνῆσαι πειράσομαι. Θέογνις γὰρ καὶ Πείσων ἔλεγον ἐν τοῖς τριάκοντα περὶ τῶν μετοίκων, ὡς εἶέν τινες τῇ πολιτείᾳ ἀχθόμενοι·
despite their claims they did not dare to carry them out, as I will try to show you by discussing first my own concerns and then yours. Theognis and Peison stated before the Thirty that among the resident aliens that there might be some who were embittered against their administration,
Lysias Speeches 12.5
In these instances we can make use of punctuation - a colon, or otherwise something like ‘namely’ to indicate that the second sentence fulfils the promise of the first. For example:
τὸν ὄντα δ’ εἴσῃ μῦθον· οἵδε γὰρ ξένοι
ἥκουσ’ Ὀρέστου πρός με κήρυκες λόγων.
ἀλλ’, ὦ ξένοι, σύγγνωτε τοῖς εἰρημένοις.
You will know the truth: these strangers
have come from Orestes carrying messages for me.
Now, strangers, forgive what has been said.
Euripides Electra 346-8
In spoken English we will often mark the link expressed by γάρ in even less formal ways. We may start explanations with ‘you see…’ or ‘after all…’, and examples with ‘I mean…’. These can often be possible translations for γάρ. For example:
μηδεὶς δ’ ὑμῶν, ὦ ἄνδρες Ἀθηναῖοι, δυσχερῶς ὑπολάβῃ· καὶ γὰρ νῦν ἀστὰς γυναῖκας πολλὰς εὑρήσετε τιτθευούσας, ἃς ὑμῖν καὶ κατ’ ὄνομα, ἐὰν βούλησθε, ἐροῦμεν.
Let none of you take this in the wrong way. After all, even now you can find many citizens acting as wet-nurses, who we can name for you, if you like.
Demosthenes Speeches 57.35ὦ τέκνον, ὦ παῖ, κἀξ ἀγεννήτων ἄρα
μῦθοι καλῶς πίπτουσιν· ἥδε γὰρ γυνὴ
δούλη μέν, εἴρηκεν δ’ ἐλεύθερον λόγον.
My child, my baby, low-born people too can be right.
I mean, this woman is a slave, yes, but the suggestion she has made is a free one.
Sophocles Trachiniae 61-63