---long post
GS1 provides many things: the (mandatory) code for recognizing the company, a database where the "model" code (numeric) can be recorded if you need other actors in the supply chain to use the same information , a website for generate images of the "barcode" - that is, the translation of numeric codes in a condensed form that can be read by a scanner (datamatrix or linear barcode)...
You are not mandated to use any of these solutions/tools apart for the company code - you just need to be compliant with their rules. All GS1 sites have lot of information about (bar)coding standard - they can be a little challenging, but you probably do not need to go in such a detail.
----theory---
Basic concept: UDI information (UDI-DI - fixed - and UDI-PI - variable) has to be represented both in clear and in a format understandable by machines (scanners). This is a usually barcode or datamatrix.
Accepted standards for barcode and datamatrix are created and maintained by GS1 , HICBBC and some others (i don't remember who is the third accredited to FDA) . These consortium established rules for coding information: they make sure that a UDI is actually unique - there cannot be two company using the same prefix, and rules forbid the reuse of already used numbers - and that the included information can be understood by anyone knowing the rule.
For GS1 this is done by writing information in a single string where each part is identified by a leading number which identify the information who follows and specific operators for dividing information.
e.g for the UDI-DI part , if defined according to GS1 standard, the GTIN code (equivalent in role, because it identify the model) should be used : the rule says it is 14-character long, it begins with the company prefix code and has to be included in the barcode with a leading string (01) and no separator at the end. Expiration data has to be included written as 6-digit number (yymmdd) and identified with a (17) leading string - correct name is Application Identifier. And so on.
Then , the string is codified in an image.
So, what their platform does is to take the plain text information you input, add the correct leading numbers and separators and representing the resulting string as an image.
DISCLAIMER: rough explanation, do not base any implementation just on this.
----end of theory ---
Their website/application is not the only software doing this, for sure it gives guarantee about a correct result .
In our company, we have to do a little bit of adjustment but the ERP system we use (quite a basic one) is able to generate images for the barcodes and print them. Other solutions, as said, are to have a separate software (installed in your computer) who generates the images basing on the input data or have a specific printer generate the image basing on the string you provide - you just need to be sure the software/system you use can generate "GS1 datamatrix and not simply "datamatrix" . I think the most flexible solution is to have a software installed because it can have its database or interfacing with another one, and is usually endowed of the "string encoding" features.
As said by japayson, search for barcode software (better for "GS1 datamatrix software") : quite all of them has options for managing data and producing bar codes compliant with GS1 standard, which is a subset (variant) of a barcode codified in ISO standards. e.g. see
GS1 data matrix
Obviously, any barcode software cannot know what information has to be included in the drawing if you do not provide them
----end of long post , hope it was helpful