Laravel 5.4 - Updating a resource

you should use

{{ method_field('PATCH') }}

as your form field

and change action to

/posts/{{ $post->id }}

like this:

<form method="POST" action="/posts/{{ $post->id }}">

        {{ csrf_field() }}
{{ method_field('PATCH') }}
        <div class="form-group">
            <label for="title">Title</label>
            <input name="title" type="text" class="form-control" id="exampleInputEmail1" aria-describedby="emailHelp" value="{{ $post->title }}" required>
        </div>
        <div class="form-group">
            <label for="description">Description</label>
            <input name="description" type="text" class="form-control" id="exampleInputPassword1" value="{{ $post->title }}" required>
        </div>

        <div class="form-group">

            <button type="submit" class="btn btn-primary">Update</button>

        </div>

    </form>

There are a couple of things you have missed out.

Firstly, as @Maraboc pointed out in the comments you need to add method spoofing as standard HTML forms only allow for GET and POST methods:

<input type="hidden" name="_method" value="PATCH">

or

{{ method_field('PATCH') }}

https://laravel.com/docs/5.4/routing#form-method-spoofing

Then you will also need to omit the "edit" uri in your forms action:

<form method="POST" action="/posts/{{ $post->id }}">

or

<form method="POST" action="{{ url('posts/' . $post->id) }}">

https://laravel.com/docs/5.4/controllers#resource-controllers

(scroll down a little bit to the Actions Handled By Resource Controller section)

You also may find it helpful to watch https://laracasts.com/series/laravel-5-from-scratch/episodes/10

Hope this helps!