Function parameters out of nowhere?

You are passing a function to another function, this

function(req, res) {
}

is a function. Assuming you gave it a local variable name like b in the called method, the function could then be invoked. As an example, -

app.get = function(a, b) { // <-- assign a function to app.get
  b("one", "two"); // <-- and then req would be one, and res would be two.
}

This is actually found here:

app.listen = function(){
  var server = http.createServer(this);
  return server.listen.apply(server, arguments);
};

As you can see, express() is this and it is being used as a parameter to createServer.

You can find the documentation of createServer here:

The requestListener is a function which is automatically added to the 'request' event.

Then when you check the request event here:

Event: 'request'

function (request, response) { }

Emitted each time there is a request. Note that there may be multiple requests per connection (in the case of keep-alive connections). request is an instance of http.IncomingMessage and response is an instance of http.ServerResponse.

Technically this event gets emitted every time a new request from a browser is received.

And this code

app.get('/home', function(req, res) {
    // req and res are objects
})

Is somewhat a listener for a request to this route (check expressjs source code).

So req and res are short-hand of request and response and are passed from the request event.

Then express added some more methods/properties found here and here.

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If you want to see the code for .get(), see here.