an admission of error or discourtesy accompanied by an expression of regret
(+ for) a poor substitute; a specimen
an apology for a tail
an excuse or explanation for, or vindication of, something; an apologia
I offer no apology for my lengthy introduction
(in pl) a formal expression of regret that one is unable to attend a meeting, etc
send one's apologies
[via French and late Latin from Greek apologia a speech in defence, a vindication, from apo- + logos speech]