An abecedarius is an acrostic

Acrostic

An acrostic is a poem or other form of writing in which the first letter, syllable or word of each line, paragraph or other recurring feature in the text spells out a word or a message. As a form of constrained writing, an acrostic can be used as a mnemonic device to aid memory retrieval. A famous...

 in which the first letter of every word, strophe

Strophe

A strophe forms the first part of the ode in Ancient Greek tragedy, followed by the antistrophe and epode. In its original Greek setting, "strophe, antistrophe and epode were a kind of stanza framed only for the music," as John Milton wrote in the preface to Samson Agonistes, with the strophe...

 or verse

Verse (poetry)

A verse is formally a single line in a metrical composition, e.g. poetry. However, the word has come to represent any division or grouping of words in such a composition, which traditionally had been referred to as a stanza....

 follows the order of the alphabet. Abecedarius is also a generic term for an alphabet book, which dates back to Biblical writings such as the Psalms

Psalm 119

Psalm 119 is the longest psalm as well as the longest chapter in the Bible. It is referred to in Hebrew by its opening words, "Ashrei temimei derech" . It is the prayer of one who delights in and lives by the Torah, the sacred law...

, which used successive letters of the Hebrew alphabet as the first letter of each stanza.

Examples

A Bear Climbed Down

East From Great Height

In Jest Killing Lame

Millipedes Never Offending

Pretty Queens Realizing

Somewhere That Umbrellas

Visit Well-tuned Xylophones

Yearly Zimmerman

Although Big Chefs Don't

Eat For Good Health

In Jest Kids Like

Making New Organic Pizzas

Quite Readily Served To

Unassuming Villagers While

Xylophonists Yodel Zanily

A Black Cat Danced

Even For Good Hearing

Iguanas Just Kites Lay

Many New Octopuses Print

Queens Ready Sometimes The

Underside Vacuums While X-rays

Yell Zanily