React-router with BrowserRouter / browserHistory doesn’t work on refresh

First thing you have mentioned in your routes as the home component to have path /home. So you need to visit http://localhost:8080/home. Also if you try to access this url directly, it will give you this error since you are using browserHistory. If you want you can use hashHistory or HashRouter in react-router v4, in which case you will need to visit http://localhost:8080/#/home. If you want to continue using browserHistory or BrowserRouter as in react-router v4, then you will need to add historyApiFallback: true in you webpack

var webpack = require('webpack');
var path = require('path');

var BUILD_DIR = path.resolve(__dirname, 'src/client/public');
var APP_DIR = path.resolve(__dirname, 'src/client/app');

var config = {
    entry: [
        APP_DIR + '/config/routes.jsx',
        'webpack/hot/dev-server',
        'webpack-dev-server/client?http://localhost:8080'
    ],
  output: {
    publicPath: 'http://localhost:8080/src/client/public/'
  },
  devServer: {
    historyApiFallback: true
  },
  module : {
    loaders : [
      {
        test: /\.jsx?$/,
        loader: 'babel-loader',
        include: APP_DIR,
        exclude: /node_modules/,
        query: {
            presets: ['es2015']
        }
      },
      {
        test: /\.scss$/,
        loaders: [ 'style', 'css', 'sass' ]
      }, 
      {
        test: /\.json$/, 
        loader: "json-loader"
     }
    ]
  }
};

module.exports = config;