When you search from the TF search page, it requires you to fill out more than just the keyword field, even though the other required fields are already set to a default (like Search All Open Forums) that you usually don't change. So if you were to just submit a keyword from a sig search directly to the TF search page, it would give you an error message because it thinks that you submitted a query from the TF search page without filling out all the required fields. The www.srsyo.org/tfsearch.php
script fills in the required fields for you (with the usual defaults, like searching all the forums and all dates) and then redirects you to the TF search page.
Um... that was a really unnecessarily complicated explanation, but basically the tfsearch.php script is just there so that you don't have to put all the required fields in your sig.