It's used to emphasize the intensity of something, much like the English word "so" or "very".
Here are some examples:
* "Il fait tellement chaud!" (It's so hot!)
* "J'ai tellement faim!" (I'm so hungry!)
* "Je suis tellement contente de te voir!" (I'm so happy to see you!)
"Tellement" can be used with adjectives, adverbs, or verbs to intensify their meaning.