Routing refers to determining how an application responds to a client request to a particular endpoint, which is a URI (or path) and a specific HTTP request method (GET, POST, and so on)

Here is an example about a route for GET method

app.get('/example',
    function(request,response){
        response.send('I am example');
        console.log('I am example');
    }
);

The first parameter (/example) is the route and the function is the callback. And the url might be something like http://localhost:3000/example. If you add parameters after the route like this

app.get('/example/:name',
    function(request,response){
        response.send('Hello '+request.params.name);
    }
);

Then you have to send the request like this http://localhost:3000/example/Jim

And if you need to use two parameters in GET-request, you can use this syntax

app.get('/example2/:firstName/:lastName',
    function(request, response){
        response.send('Hello '+request.params.firstName+" "+request.params.lastName);
    }
);

Then you can send the request like this http://localhost:3000/example2/Jim/Jones

And also you can use below syntax for two parameters GET-request

app.get('/example2/:firstName&:lastName',
    function(request, response){
       response.send('Hello '+request.params.firstName+" "+request.params.lastName);
    }
);

Then you can send the request like this http://localhost:3000/example2/Jim&Jones

Here is an example about route for POST method

app.post('/',
    function(request,response){
        response.send(request.body);
        console.log(request.body);
    }
);

Above function will response with the same data that you send inside the HTTP body.

Middleware functions are executed after every incoming request. Below is an example about middleware function

app.use(
    function(req,res,next){
        console.log('The common middleware called');
        next();
    }
);

So, below middleware is executed after every request to every routes. You can also add a path to the middleware.

app.use('/example',
    function(req,res,next){
        console.log('The example middleware called');
        next();
    }
);

So, the above middleware is executed when request to path example comes.

The next function is a function in the Express router which is used to execute the other middleware functions succeeding the current middleware.