Several reasons, but it mostly comes down to efficiency and giving them a more uniform view of the candidates.
- They will typically scan (automatically) your application looking for certain key words to exclude candidates who don't include enough keywords in their application form (eg if none of "Software", ".NET", "Databases", or "Web" are in there, you probably aren't suitable for an ASP.net development role)
- They don't want their staff having to open attachments from unknown sources on a publicly facing website. Or at least, not un-necessarily (ie at early stages), as this likely involves some overhead of using secured machines separate from their corporate network
- They have their own internal system for storing applications, and having the contents entered into that in plain text is much easier for them to handle
- It allows them to exclude information they don't primarily care about (hobbies etc, perhaps), allowing them to focus on their core requirements
- It allows them to show and compare multiple candidates on the same screen, or in a directly comparable format. "Show me Jenna, Tom, and Sandra's qualifications side by side. Okay forget Sandra, how about Paul?", for example. This is much harder to do with a bunch of word documents and PDFs.
Fundamentally, it comes down to the fact that they have some kind of process for handling your application which is more automated than simply reading CVs and throwing them into "Yes", "No", and "Maybe" piles.
They'll often ask for a digital copy of your CV because the automatic scanning (#1) and manual checks against the plain-text version (#3) are typically only used to make the longlist/preliminary shortlist, while keeping their system as safe as possible (#2) from viruses etc. By only asking for specific information (#4) they can keep the process as efficient and concise as possible.
Once they've got the shortlist they'll often then use your actual CV to make the decision on which applicants to take forward, as the CV is better formatted and shows your presentation and any additional information you've chosen to include (eg hobbies) which may now be relevant for distinguishing between shortlist candidates, but were irrelevant when simply trying to exclude unqualified applicants.
And finally, the information you provided will often (if you get the job) end up on your personal record somewhere, in which case they want it in a text format, not tied up in a word document.