Simply put, constructing sentences using parallel structure is a way of making wording match. When we make wording match, we create clearer, economical, elegant sentences that are much easier to read.
Let's take a closer look at your example sentence on your worksheet for a better understanding. The following sentence is not parallel because verb types and tenses do not match:
Being compassionate and because she knows a lot about animals, Jessica will make a good veterinarian.
Here, the writer started the sentence with the -ing ending verb "being" in the phrase "being compassionate." But, if we look further down the sentence, we see no other -ing ending verbs.
That tells us the wording does not match.
Instead, we see the simple present tense verb "knows." So, in order to make things parallel, we must reconstruct the sentence so that all verbs are in the simple present tense:
Because she is compassionate and knows a lot about animals, Jessica will make a good veterinarian.
In the revised version, both "is" and "knows" are simple present tense verbs, so we know that everything matches and we have achieved parallel structure.
Let's take a closer look at the third problem on your worksheet to see exactly why the wording in the sentence is not parallel:
Mrs. Shapiro had heard about the new hockey league but not that there would be a team in Greensboro.
In the first half of the sentence, we see the phrase "heard about," but in the second half of the sentence, we see the phrase "that there would be." Words in a sentence carry over in meaning, so if we carry the verb "heard" to the other half, we get, "heard that there would be." As we can see, the phrase "heard about" does not match the phrase "[heard] that." In order to make things match, we must use one of these words twice. We would not want to use the word that twice because there is a standard grammar rule stating we always want to avoid using the word that more than once in the same sentence. Therefore, we are left with creating our parallel structure by repeating the word about. Repeating the word "about" would yield the following parallel structure:
Mrs. Shapiro had heard about the new hockey league but not about the new team in Greensboro.