Let's do some philosophy. Pick up an object - it could be your phone or a pen - and put it right in front of you, so that it's in the centre of your vision. Notice the colour of the object (I'll assume that it's a blue pen for now). What's going on when we're looking at it?
First, we know from neuroscience that the cones and rods in our retina receive photons reflected from the pen at various wavelengths, stimulating signals via our optic nerve to the brain. Crudely speaking, the brain then processes these signals into representations of the colours we see.
However, if you were born in a completely black and white universe - i.e. the desk in front of you is black and white; the pen is black and white - then it's difficult to see how all this neurophysiological knowledge of the causal structure of sight could tell you what it'd be like to see the blue pen.
Next, imagine that your twin from the Colour-Universe steps through a mysterious portal into your black and white room. Your twin is holding the blue pen from the first case. It seems that you've gained a kind of knowledge not captured by the neurophysiological picture - namely the experience - the "what-it's-likeness" of seeing the colour blue for the first time.
Now, whatever you might conclude from this case, notice what we've done. We've just used a rational method called "elimination" to test a claim about the purview of neuroscience.
We've eliminated our ability to experience colour from our conceptual laboratory, and noticed that the standalone neurophysiological description of colour seems exhausted when we try to use it to describe that experience. One conclusion we might infer from this is that neuroscience only captures one part of the picture of the nature of experience - namely structure.
Now, there's a wealth of literature on how to respond to this view, and it's not clear to me that adopting views on either side leaves you any better off.
But one thing is clear: we should want to answer the question because, if the above conclusion is true, then we might need to look elsewhere for a completed picture of certain features of reality. But, if it's false, then we might either (i) need to discover a purely scientific explanation for experience which dissolves the problem or (ii) radically adjust our conception of science altogether to account for it.
This is just a toy-example of what some philosophers get up to.
Some science-populists, like Lawrence Krauss, say they don't have much time for philosophy since, according to them, science has outmoded it. However, given that there are several key points-of-contact between philosophy and science, I don't see much need for the kind of demarcation Krauss et al make.
Neither does Daniel Dennett, who has publicly pressed Krauss on this issue to the point where he's revised his original view to state that, whilst philosophy is intellectually interesting, it has no bearing on methodological science. I.e. philosophy of science does not contribute to data-collecting. This may be true.
But it isn't the only way philosophy could be, or indeed is, related to science. In the analytic tradition, we generally take philosophy to be a project of clarification. One way of thinking about this is that philosophy, applied in cooperation with natural science, looks like a strong contender for a complete understanding of many phenomena. That is, science can provide us with a rich picture of its causal structure, and philosophy can give us a way to think clearly and correctly about that picture.
And philosophy has very good tools of its own for this purpose. First, if a philosopher is scientifically literate, she can provide robust conceptual frameworks in which to test the logical consistency of scientific theories, the purview of their structure, and their predictive claims. In this way, philosophy can help us identify theoretical virtues and limitations.
Now, public thinkers like Sam Harris and Krauss have argued in favour of a widened conception of science which includes this kind of procedural, conceptual role for philosophy. This view of "science" has benefits - namely it unifies the two practices and, through forecasted good practice of both, each would presumably help discard messy or unhelpful components of the other.
But, one way to see that science does not simply subsume philosophy in this way is to ask yourself why you value the scientific method in the first place - if you do at all. And pay careful attention to how you answer this question. Do you answer it scientifically - i.e. run experiments and carry out empirical work? If so, you're still going to be left with the same question - why do you value empiricism over other methods of investigating your preference for science?
Whichever way you answer this, and even if you're as naïve to philosophy as one can possibly be, you're eventually going to have do so in a way which at least crudely employs some epistemology or metaphysics. Both of these fall under the purview of philosophy. And I'd argue that, if we want to be intellectually honest about our investigative practices, we shouldn't be ashamed to say this.
If contemporary philosophy still proceeded in vacuum, cut off from science, I'd agree with Krauss that it's useless. But it doesn't. And, if applied to conceptual issues in the natural sciences, it certainly has a much juicier role to play than Krauss would have you believe.