I agree with the other answers that a "defamatory" statement is one that damages someone's reputation whether or not it is true (and hence in many cases not legally actionable). "Defamatory" is a close synonym of "disparaging" (and one can contactually agree to refrain from making disparaging but true statements about someone else, something usually done in connection with a settlement agreement related to a dispute).
In modern U.S. law, the First Amendment usually makes truth an absolute defense in cases involving public figures and matters of public concern, and arguably, more broadly.
This said, sometimes true statement that imply false statements or present someone in a false light can give rise to legal liability because they are used in a misleading way.
For example, if you accused someone of killing their brother in a way and context that strongly implied a homicide or a death caused by culpable negligence, when in fact, the person turned off life support for their brother pursuant to a living will and the brother also had a DNR (do not resuscitate) order, that could conceivably be defamatory if presented with an intent to mislead.
But, this is a fairly modern legal position the only came to be true in the later part of the second half of the 20th century.
Historically, certain kinds of truthful statements could give rise to criminal libel convictions. These cases were reflects in Colorado's criminal defamation statute before it was legislatively repealed in 2012 (and after some, but not all, of these provisions were declared unconstitutional). It said before it was repealed:
18-13-105. Criminal libel.
(1) A person who shall knowingly publish or disseminate, either by
written instrument, sign, pictures, or the like, any statement or
object tending to blacken the memory of one who is dead, or to
impeach the honesty, integrity, virtue, or reputation or expose the
natural defects of one who is alive, and thereby to expose him to
public hatred, contempt, or ridicule, commits criminal libel.
(2) It shall be an affirmative defense that the publication was
true, except libels tending to blacken the memory of the dead and
libels tending to expose the natural defects of the living.
(3) Criminal libel is a class 6 felony.
Thus one exception was to speak ill of the dead, even if the statement was truthful.
The other exception was to "expose the natural defects of one who is alive, and thereby to expose him to public hatred, contempt, or ridicule," in the sense that it would be traumatizing by and towards whom it would be an incivility to state publicly those defects - like calling someone with a severe developmental disability a retard, or perhaps calling someone born out of wedlock a bastard.
This section's imposition of liability for truthful statements was held to be invalid insofar as it reached constitutionally protected statements about public officials or public figures on matters of public concern under both the state and federal constitutions, but not where one private person has disparaged the reputation of another private individual. People v. Ryan, 806 P.2d 935 (Colo. 1991). The law was clear that this was the case far earlier, but there were no prosecutions in which to test the constitutional of the case for a long time.
Historically, criminal liable also often required proof that the person making the statement had an intent to provoke a breach of the peace. Leighton v. People, 90 Colo. 106, 6 P.2d 929 (1931).
Likewise, some cases had a character akin to contempt of court, and punished "words published in a newspaper, which tend to impeach the honesty and integrity of jurors in their office" apparently without regard to the truth. Byers v. Martin, 2 Colo. 605, 25 Am. R. 755 (1875) (Byers with the proprietor of one of Colorado's leading newspapers at the time and there is still a neighborhood in Denver named after him).
Very few cases where ever prosecuted under either of those prongs of the statue, in part out of doubt about their constitutional validity.
Another exception is noted in another answer from Noonan v. Staples, Inc., 556 F.3d 20 (1st Cir. 2009). That case applied Massachusetts law in a diversity case, makes clear that imposing liability for damaging someone's reputation out of ill-will with a truthful statement. But this was a fairly marginal federal court interpretation of state law (citing state court decisions that seem to contradict this conclusion but reasoning around it), and makes clear that it doesn't apply under clear U.S. constitutional law in matters of public concern or when a public figure is involved. Also, the defendant wasn't permitted in that case to argue on appeal that the U.S. Constitution prohibited imposing defamation liability for truthful statements made about private individuals in matters that were not public concerns because the issue wasn't raised in the trial court - so the precedent does not preclude a future litigant from asserting that position in a later case.
Generally speaking, however, those categories of defamation liability no longer exist in U.S. law.