The software is Acrobat, the software that your forms were probably created in originally.
A few things.
Signatures are not supported by FormsCentral, if you distribute FormsCentral enabled version of your PDF form with Signature fields and users sign the PDF, that signature will not be submitted back to FormsCentral and you would not have any record of that signature. Supporting signatures is a popular feature request but is not something that we support at this time.
What you see when you try to Import your PDFs:
is not very clear, saying it is an invalid format is extreme... It is related to the PDF form having been created in a third-party PDF authoring application (not Adobe Acrobat) and the form is missing some "appearances" that, if we imported the PDF and allowed you to save a FormsCentral enabled version, would not look as you expect. Saving the PDF in Acrobat fixes the appearances and the PDF can then be imported into FormsCentral.
In general you do not need any other software with FormsCentral, Acrobat is very useful for being able to further edit your PDF forms after saving from FormsCentral (careful edits, there is an FAQ that talks about editing a FormsCentral PDF), and for this case where the PDF needs to be repaired by Acrobat.
If you do determine you need Acrobat, there are a few options, you can purchase the desktop software or there is also a subscription available that includes both Acrobat, FormsCentral and some other paid Adobe services: https://www.acrobat.com/acrobatplus/en/home.html