The humidity prevents your sweat from evaporating from your body like it should. So that's why you feel hotter than it is.
You're unable to cool off as good with the humidity as you could without the humidity. We sweat because it's our way of keeping our bodies cool and if the humidity prevents that then we can't cool down properly.
That's how the air conditioners keep us cool. Ever notice all the water dripping out of your air conditioner? That's the humidity in the air which is making us feel hotter.