It can all be a little overwhelming, here's what those things are
Render Functions
When Vue compiles your Vue instance, it creates a render function, which is a pure JavaScript representation of your HTML. Something like this:
new Vue({
template: `<div>{{msg}}</div>`,
data:{
msg: 'Hello Vue
}
}).$mount('#app')
Will actually turn into something like this:
new Vue({
render: function(createElement) {
return createElement('div', this.msg)
},
data: {
msg: 'Hello Vue'
}
}).$mount('#app')
Here's a JSFiddle: https://jsfiddle.net/bvvbmpLo/
You don't need to handle that, Vue does it for you, and most of the time you won't find yourself writing render functions. However, it is important to understand that Vue is doing some behind the scenes work to represent your templates in pure JavaScript.
Virtual DOM re-render and patch
You really don't need to know about this, but Vue uses a virtual DOM, because it's is easier to track changes and decide which parts of the DOM need updating.
In reality, what happens is that Vue builds up a tree that represents the DOM (called a vTree), then when you change state it uses something called a diffing algorithm which compares the previous vTree to the current vTree as it now stands, and attempts to figure out which part of the page it needs to change to reflect that state in your view. The changing of a small part of your page to represent the new state is called patching.
That's a pretty high-level overview of a virtual DOM, it's fiendishly complex to get this working efficiently which is why frameworks like Vue exist in the first place. If you're interested in learning more about that then try taking a look at Matt-Esch/virtual-dom on Github, which does a great job of explaining this concept in more detail.
