Sweat
To sweat is to cook vegetables over low heat in a pan with fat. This allows them to soften but not turn brown and for the juices from the vegetables to be concentrated in the fat.
Fun related videos
Sweating Vegetables

How to Sweat Vegetables | It's Only Food w/Chef John Politte

Sara's Cooking Tips: How to Sweat an Eggplant
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Sweating Vegetables
Source: Sizzleworks Cooking School
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How to Sweat Vegetables | It's Only Food w/Chef John Politte
Source: It's Only Food w/Chef John Politte
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Sara's Cooking Tips: How to Sweat an Eggplant
Source: MAFieldtoTable