Here’s what’s so hard to know about the Dance Theatre of Harlem: The thing that makes it work. Go on about technique and strength and talent if you must. Certainly all of that was in place Saturday when the troupe showed up at the Maine Center for the Arts. But it’s rather pretty to think that, with all those elements praiseworthily in place among the dancers, there’s something a good deal smaller that draws the eye and calls the spirit.

In a piece such as “Sasanka,” it could be that South African choreographer Vincent Sekwati Mantsoe knows about the funky order and the merry chaos of human existence. With Ondekoza’s breathy traditional instruments setting the beat, the dancers transformed into unbridled animals — both human and brutish. They froze in Gauguin-like tableaux, and then stalked forward to the next captivation.

You might find yourself using words such as strut, wiggle, jiggle and jounce to convey a sense of this piece. Yet, it may have been the ornate attention to hands that, in a silent and lingering way, grabbed hold of your fascination and massaged it toward an understanding of Mantsoe’s exuberance in the rawest of life forces. The flutter of fingers, the tightness of fists and the whirling angularity were the tiny details that stuck after all the bigness of this mythic piece ended.

John Alleyne’s neoclassical piece, “Adrian (Angel on Earth),” took advantage of a similar transformative style. Inspired by James Thurber’s comment about “rare souls whose spirits get magically into the hearts of men,” the troupe engaged in courtly dances about the invincibility of true love. A certain disregard for gravity marked this piece, but, more importantly, there was a blithe tenderness. Although Timothy Sullivan’s plunking piano music may have been too loud for most ears, it underscored the boldness of the “ineffable and eternal thing” that happens when people share their bliss.

The final section of “Adrian,” in which the male dancers performed pas de deux with one another, was about as delicately stunning as dance gets. To witness powerful men treating each other with kindness and vulnerability was disarmingly beautiful.

The evening’s tour de force, however, was “Dougla,” a choreography in which Eastern and African symbols meet. The recurring detail of this piece was a single forefinger held forward — sometimes as a warning, sometimes as a reprimand, sometimes as a silencer. Created by Geoffrey Holder (who many may remember as the bald Caribbean spokesman for 7-Up commercials many years ago), “Dougla” was acrobatically ritualistic.

There was always a sense of having mistakenly come upon a tribe of people deep in the secret ceremonies of their lives. A juju woman, a wedding party, a mind-boggling contortionist, and the ever-present cycles of the sun and the moon (in the lighting of the backdrop) allowed these most-amazing dancers to tell a story about the energetic convergencies in community life.

Dance Theatre of Harlem is one of America’s most important companies in regard to aesthetic vision and historical significance. But pinning down the precise effect of any individual choreography is not so easy. Perhaps it’s enough to say that Dance Theatre of Harlem has everything to do with the combination of discipline and joy.