Translation:There are letters from several people here.
The key to the difference is the word "the" in your suggested sentence -- "Here are THE letters from several people."
"The" is a definite article, and including it means we're talking about some particular letters that we know something about already. For example, "Here are the letters from several people... that Matěj told you about yesterday." "... who want to nominate you for the Nobel Prize." "... which were mailed from outside the UK." in contrast, the sentence in this exercise simply refers to "letters from several people" that happen to be "here."
As VladaFu mentioned, an accepted translation that is very similar to your suggested sentence is "Here are letters from several people." It is almost identical to yours, but it does not include the word "the."
Would someone who knows Czech please tell me what TADY refers to in the original Czech sentence-- letters or people? If the former, then "There are here letters from several people" should be accepted (it was not). If the latter, HERE can go at the end, as in the accepted English translation.