I asked ds on the way to school what a fronted adverbial is. He says it's the first part of the following sentence (up to the comma) "Running into the garden, the squirrel picked up his acorns". I have no idea whether he is correct.
Yes, that's correct. The same sentence could be written as e.g. 'The squirrel picked up his acorns running into the garden' which may make you wonder whether it was the squirrel or the acorns running.
The 'running into the garden' is an adverbial clause (as it has a verb in it) telling us when the squirrel picked up the acorns. When you move this adverbial clause to the front of the sentence, it becomes a 'fronted adverbial'. Fronted adverbials have to be separated from the rest of the sentence with a comma.
A fronted adverbial could be just one adverb, e.g. 'He jumped out of bed quickly' would become 'Quickly, he jumped out of bed', or a phrase, e.g. 'Children read their books in silence' would become 'In silence, children read their books'.