The body produces sweat in an attempt to cool us off. As it evaporates, we should get cooler. High humidity means less sweat evaporates, so not only are we not cooled, but our body produces more sweat, making us feel sticky and hot.
There are two main reasons.
Water evapourates at all temperatures and the rate of evapourating is more at higher temperature .While the water evapourates , it absorbs a lot of heat energy from the surrounding . Thus the water vapour contains/retains an amount of heat more than the same mass of water at the same temperature. This is called the latent heat of vapourisation. Thus 1 kg of water vapour retains about 2260 Kilo Joules of heat more than the same mass of water or more so about the surrounding dry air. The water, while condensing gives out the Latent Heat of evapouration to the surrounding.
Therefore the quantity of heat is more in humid weather than that in dry weather at the same temperature.Thus air and the diffused water vapour together they can retain more quantity of heat than in a dry weather. Thus the air looses its quality of absorbing the heat but it may release the heat , which discomforts our body in the humid weather.
Any wet substance, easily looses its water through evapouration in dry whether and while evapourating it absorb a lot of heat in the formm of latent heat of evapouration. This makes the human body feel a sense coolness, as the swetting and evapourating process acts like temperature conditioning.If the air/ weather is humid, the process of evapouration of swetting is retarded as the air is satutrated with humidity. On the other hand the humid air while condensing releases the heat on the surrounding . This results in recieving additional heat, resulting in running of swetting and perspiring without evapouration. All this results in an uncomfortable situation due to humidity.If you go to a tropical coastal region this experience is quite normal.
One of the ways in which body maintains its temperature is through the systems of sweating. when the weather is hot we tend to sweat more. The sweat released by the body gets evaporated absorbing heat of the body for evaporation. The rate of evaporation of the sweat, and therefor the rate of cooling of the body is inversely related to the relative humidity of the air around the body. In hot and humid weather the body releases the sweat, but it does not evaporate fast enough due to higher relative humidity. Therefore we feel the heat more. The feeling of discomfort is also increased due to the unevaporated sweat which creates a feeling of stickiness.