The word stanza in Italian means ‘room’ and groups of lines are often gathered with white space between them thus forming the rooms of the poem. Hence their name stanzas.

Lines are different to sentences in that they usually do not go the full width of the page, they are used by the poet to breakdown meaning into smaller units of meaning, sound and sense. The break in the line is chosen by the poet and turns the reader back into the poem.

The craft of poetry has traditionally concerned itself with the sounds of the words and the meaning, but poems are also written, and the patterns developed in that visual field can't be overlooked if we are to concern ourselves with the full potential of the poem's structure.
The sound patterns of a poem are concerned largely with the rhythm and tone of the word. Visual pattern and variation are geared more toward the poem's placement on the page although it will affect the way it is read too.
When a poem works as it should everything fits together, and all the elements work together.

Like a painter at a canvas, the poet when concerned with the visual patterning of the poem looks at how the poem sits on the white canvas of the blank page and how that visual structure creates patterns that can be used to create a richer poem.

It has been suggested that an empty page represents silence which the poem displaces and it's true, we use the space at the end of lines and between stanzas as spaces for our readers to pause, to reflect on what has just been said. We also use the white space of the page when we indent lines, break lines, move lines inwards. Use of white space should be planned carefully as part of the poems form and not just be serendipidous. Poets should read their work aloud and consider how the pauses caused by white space affect rhythm, flow and meaning.
The poem on the page.
Prose is written in sentences that fit the page and so it automatically looks tidy, compact and neat.
Poetry is written in lines, broken to enhance meaning, sound and rhythm, the poem should consider all these aspects when constructing lines and stanzas but they should also consider what the poem looks like on the page. Poems need to invite a reader in and if they have an uncordinated straggly appearance then they are less appealing.
Look at the visuals of the poem below with line and form broken differently.

Version 1
In cyberspace there is a race of people who want a different space

Who need to add a layer on

Too meet new friends not take them home

Some of them just pass us by touch our lives

but make us cry

Others linger sharing stories of life and love and other glories

For some the magnet feels so strong

The story weaves right or wrong

In cyberspace there is a place to meet new friends.

Version 2
In cyberspace there is a race

Of people who want a different space

Who need to add a layer on

Too meet new friends not take them home

Some of them just pass us by

Touch our lives but make us cry

Others linger sharing stories

Of life and love and other glories

For some the magnet feels so strong

The story weaves right or wrong

In cyberspace there is a place

To meet new friends.

Here is a poem by Miroslav Holub as you will see it on most websites

Go and open the door.

Maybe outside there’s

a tree, or a wood,

a garden,

or a magic city.

Go and open the door.

Maybe a dog’s rummaging.

Maybe you’ll see a face,

or an eye,

or the picture

of a picture.

Go and open the door.

If there’s a fog

it will clear.

Go and open the door.

Even if there’s only

the darkness ticking,

even if there’s only

the hollow wind,

even if

nothing

is there,

go and open the door.

At least

there’ll be

a draught.

The Door by Miroslav Holub

Go and open the door.

Maybe outside there’s

a tree, or a wood,

a garden,

or a magic city.

Go and open the door.

Maybe a dog’s rummaging.

Maybe you’ll see a face,

or an eye,

or the picture

of a picture.

Go and open the door.

If there’s a fog

it will clear.

Go and open the door.

Even if there’s only

the darkness ticking,

even if there’s only

the hollow wind,

even if

nothing

is there,

go and open the door.

At least

there’ll be

a draught.

This is how it was designed to be read. It adds another dimension.

In both of these poems the poets have chosen short lines and some lines have been indented. Lines of poetry are typically aligned to the left side of the page, but poets sometimes indent lines (move them away from the lefthand margin) in order to complicate traditional line breaks. Indentation does not mean that a line is not properly broken. Rather, the indentation, much like a line break itself, further informs the phrasing or rhythm of the poem. For example, a line that is indented more than others on the page might be read as having a slightly longer pause preceding it, or a delayed beginning, as though the poet is catching his or her breath.Or wanting to emphasis a word or phrase.
Why do you think the poets have chosen the formats and line breaks that they have? Does the change in formatting change meaning?

What can you take from this to use in your own poetry.

Use of line breaks
Writers use line breaks because it's part of what makes a poem a poem. By inserting more white space into the text, poets are able to exercise a greater degree of control over the speed and rhythm at which their poetry is read, thereby distinguishing it from both everyday language and prose literature. So in many ways, the question of "why writers use line breaks" is no different from the question of why people write poetry at all.
But that leaves the question of how poets use line breaks to achieve different effects, and the answer to that question can sometimes seem to have as many answers as there are poets writing today. Most commonly, though, writers use line breaks to determine a poem's speed and rhythm. For example, a poet may choose to use shorter lines and more line breaks in order to slow readers down and ask them to pay extra careful attention to each individual word that is being used. On the other hand, a poet may use long lines if the style of the poem is more conversational or if the sentences contain complex ideas with many clauses, since longer lines are easier and faster to comprehend. Ultimately, line breaks can be used in any way the poet desires to alter how the text of a poem is delivered to the reader.

Learning pause.
Consider when line indentation and dropped lines may work in your poetry.
Line Breaks and Syntax
Poets need to think about where lines are broken. Sometimes a sentence is divided over a whole stanza or a whole poem and the poet has to make breaks that enhance meaning sound and rhythm.
It is also important to think of the position of the end of the line this space is a place we pause, that word will resonate with us so poets need to make line breaks so the end words have key meaning.
Syntax is a term that refers to the structure and word order of a sentence. Generally speaking, poets place line breaks within their poetry so that they don't meaningfully disrupt the syntax of the sentence, but instead create pauses that mimic the natural pauses of speech. However, this not always the case; some poets use line breaks to intentionally create an unusual cadence or phrasing in their poems. Using line breaks in these two different ways produces a very different effect.
Using line breaks well makes a tremendous difference to the sense, sound and meaning of poems.