When history of PHP starts, it was standard, that HTML was generated directly inside PHP scripts. But it happen to generate some problems when it grown to one of most popular ever web programming languages.
To keep people working in huge projects comfortable with their tasks ie. when developing web services, where was an MVC architectural pattern invented. M for Model is used to store data and handle them in a maintainable and repeatable manner. V for View as an part, that is responsible to generate proper output. C for Controller that are responsible for sending commands to models etc., being a core logic of application.
When user send a command to service, Controller is handling it and understanding. Triggering changes on proper Models and maybe forwarding actions to other Controllers as long as View Controller is reached. View controller takes a proper view, injects into it generated data and executes it to create output that is send back to user. If template for view is not yet generates, it triggers template engine to do it.
Proper implementation of full MVC greatly helps both programmers, system architects, front-end devs etc. But when on one side it happen difficult to maintain databases (so ORM were developed), on other side of system it was difficult to maintain views.
One of principles of MVC is that Logic (with huge "L") is only in controllers. So there is no logic in views. Using template engine enforces easiness of achieving that because of poor support of logic by them self. It is not a secret, that programmers are "lazy" - so if they have an occasion to put some more advanced logic into view, they would do it.
I guess that all frontend devs have programming skills. Problem is to make them stay with you. Working on huge project with lots of views (and so hudge templates) with PHP mixed into them will drive them crazy. It is much easier to read code written for template engine.
Idea of template engines is to add one more part to system, that offers possibly simple language allowing to use basic logic like loops and if statements. On one side template engine receives kind of a textual file to transform it into PHP file with mixed into it hyper dose of all important HTML.
If you are alone developer, it is important to nobody that you are using files that mixes PHP with HTML. It looks probably close to this:
<html>
<head>
<title><?=$title?></title>
<? foreach($metas as $meta) { ?>
<meta name="<?=$meta['name']?>" content="<?=$meta['content']?>"/>
<? } ?>
But any frontend developer would rather like to work on file looking this way:
<html>
<head>
<title>{{ title }}</title>
{% for meta in metas %}
<meta name="{{ meta.name }}" content="{{ meta.content }}" />
{% endfor %}
for it higher readability. It happens extremely handy when template includes some kind of javascript inlined. After all, you end up with same file you can create by hand, but this file is generated for you and stored, so it is no more generated as long, as core file is not changed. We are generating our templates during deploy what has 0 hit on performance, especially now, when Volt engine is written in C.
Another handy thing about template engines is that (with some your effort) it is possible to generate templates minified on the fly. You wont ever minify your hand-crafted template, except when planning to commit suicide.
So globally, it is a case of:
so you could pass .volt files to a front-end guy
but it is an effect of working in MVC pattern. And Phalcon is made to fulfill MVC principles. I'm not even trying to guess, how you managed to work with this piece of software for ~2.5 years not using template engine. Maybe you are working alone.