Functional resumes are good when you have little to zero work experience (or new grads). This type of resume allows you to showcase skills that fit in with the job requirements. Fair warning: most recruiters and hiring managers dont like this format and feel as though you may be hiding something. If you have a chronological resume you do not want to have one part chronological and one part functional because it will throw off the entire formatting and may confuse the employer about your skill set.
There are millions of resumes being uploaded to job sites and because of this job sites have an ongoing need for more and more web servers. Job sites earn revenue from recruiters and employers that are subscribers and not from job seekers so it makes sense to eliminate this cost and pass it on to the resume website provider. Since people manage multiple resumes in their profiles to apply for different jobs it would be better for everyone if job seekers had multiple links to different resume pages instead of resume PDFs. The storage cost to job sites is eliminated and job sites can reduce their fees to subscribers.
Combination resume is the combination of above two formats. It is getting popular these days as it includes the features of above resume formats. Just like the resume formats, there are different types of resume samples. Combination, functional and chronological are the three main types in which samples are provided on most online websites.