To swelter is to be hot — very, very hot, like on a humid, ninety-degree day. To swelter is to feel like you're in an oven.
This word is most often seen in the form sweltering, as in "The weather is sweltering! It's been over 95 degrees for a week straight." Any form of swelter is going to involve major heat — enough heat to make you sweat buckets. The opposite of swelter is "freeze."