PHRASES
explain oneself expand on what one has said in order to make one's meaning clear.
n
give an account of one's motives or conduct in order to excuse or justify oneself: he was too panicked to stay and explain himself to the policeman.
[New Oxford Dictionary of English]

rechtfertigen
b) <r. + sich> sich gegen einen Vorwurf verteidigen; sich verantworten: sich vor jmdm. wegen etw. r. müssen; Ich rechtfertigte mich mit einer kecken Lüge (Frisch, Stiller 186).
© 2000 Dudenverlag

@Daniel: sorry, the discussion you quote does not have enough substance for me. Please try to provide dictionary entries as indicated above the form for new entries and in this thread:
related discussion

explain yourself verb [R]
to give reasons for your behaviour:
He hadn't been home for three days so I asked him to explain himself.
(from Cambridge Advanced Learner's Dictionary)

und der schon erwähnte Duden-Eintrag
b) <r. + sich> sich gegen einen Vorwurf verteidigen; sich verantworten:
sich vor jmdm. wegen etw. r. müssen; Ich rechtfertigte mich mit einer kecken Lüge (Frisch, Stiller 186).

@Doris: I'm sorry as well. As a lexicographer myself, I admit my quotation was far from being perfect for a new dictionary entry. To "explain myself" :-) - I just wanted to swiftly react to the discussion I had read...

I also admit that "to explain oneself" and "sich rechtfertigen" do not have 100% same meaning in all cases, but I can't think of a more precise translation.