ξηγιέμαι is a slang form of the verb εξηγούμαι (=to explain oneself; to settle one's accounts with someone).
ξηγιέμαι usually means to level with someone or to be on the level with someone.
It is usually followed by καλά, e.g. Πάντα ξηγιέται καλά. He's a real on-the-level guy.
Here the lyricist has gone for φρόνιμα (in a well-behaved manner; in a prudent manner) as it also suited the meter better.
Therefore ξηγήσου φρόνιμα και μη με κατακρίνεις (the imperative form) actually means "act wisely / do the clever thing and do not blame me".
