Proteins denaturate when they lose their three-dimensional structure and their folding with it. Enzymes lose their catalytic activity, because the substrates cannot bind to the active center anymore. Some, but not all, proteins can regain their correct structure when the denaturating influence vanishes.
The denaturation of nucleic acids such as DNA, also called melting, is the separation of a double strand into two single strands, which occurs when the hydrogen bonds between the strands break down. Nucleic acid strands will realign when "normal" conditions are restored.