Here is an example for string:

echo urlencode_deep( 'foo bar' );

// Output will be: foo+bar

Here is an example for array:

$data = urlencode_deep( array( 'foo' => 'bar long text', 'key1' => 'value1' ) );

// Output will be for $data: array( 'foo' => 'bar+long+text', 'key1' => 'value1' )

Here is a use case for multi word string as url parameter:

echo add_query_arg( 'key', urlencode_deep( 'long value' ), 'http://example.com/' );

// Output will be: http://example.com/?key=long+value

Here is a use case for an array multi word string as url parameter:

$params = array( 
    'key1' => 'value1 long text',
    'key2' => 'value2',
);

echo add_query_arg(
    urlencode_deep( $params ),
    'http://example.com/?'
);

// Output will be: http://example.com/?key1=value1+long+text&key2=value2

It’s making spaces between word, if string has space:

echo add_query_arg( 'key', 'long value', 'http://example.com/' );

// Output will be: http://example.com/?key=long value