You're also jumping around in your position - first it's "meditation is sleep" now it's "meditation is time you're not stressing". Sleep does more than just allow you to escape stress. The latter is more like comparing meditation to escapist entertainment.
The simple explanation for mindfulness' effect is it allows you to better observe and understand your own mental processes. If you try to spend 10 minutes focussing on your breath, you train yourself to notice when your attention slips away. This is useful in regular life, but it also allows you to see what your attention is slipping towards - whether that's a stressor, or an unprocessed emotion, or some nonsense that you keep thinking about but can let go of once you recognise it. There's a strong benefit to living more actively in the present, as opposed to being trapped in your worries and imagination.