Actually, archival is just remote storage of data. A backup is redundant storage of data. Archival is when you don't store data on your computer due to, say, a lack of space. Data stored solely on a NAS, for example, is archived. A backup is data, either on your computer or archived, that is duplicated and stored elsewhere, sometimes in a different format, so the duplicate can be used restore the original data should it ever be lost or corrupted.
Carbonite is a "cloud solution" that can meet both jimbo's definition of archival and backup. It has unlimited backup capacity (the only caveat being the throttling that I mentioned before above a certain volume). It is not a single solution, however, nor should anyone expect any solution to be a single solution. The initial backup to Carbonite can take days to weeks, depending on the initial volume, the speed of one's internet connection, and how long one's computer runs each day (mine runs 24/7 unless I'm out of town). As long as a file remains on your computer, Carbonite will retain it. Even if the computer is offline for long periods of time, Carbonite will continue to retain the file (assuming you keep paying the bill; my last desktop was offline for several months and I didn't lose any data). Once the initial upload has been done, the data remains until it Carbonite detects that it has been changed or deleted; then, thirty days later, the changed or deleted data will be deleted from Carbonite's servers.
As jimbo pointed out, cloud solutions with huge amounts of data will take huge amounts of time to recover, which is one of many reasons why cloud backups should never be relied on as a sole backup or for sole archival (archival meaning the only place where one's data is stored). Another reason cloud archival or backups should not be a sole solution is they can fail. Free cloud sites have a history of being ephemeral; they can disappear, usually with little or no warning. Paid plans are usually more reliable. Business plans are fastest and are the most reliable but are also expensive. they are geared toward businesses that need large, daily uploads and fast retrieval if local data is lost. Usually, business plans will store one's data on redundant servers whereas home plans will store data on only one server. Business cloud backup plans are geared for new businesses and ones too small to cost effectively maintain offsite servers. Home plans are usually slower and don't have the server redundancy that the more expensive business plans do. But even paid cloud backup solutions still can fail, same as any other media one can use to store backups on.
Jimbo is correct in that static information needs to be backed up but once but redundancy is still vital and the backups still needs to be maintained to ensure the media the backup is kept on hasn't failed. Even though the main HDD (as I call it) in my computer has static information that will rarely, if ever, change, I re-back it up on a weekly (or more frequent) basis simply because it is easier for me to do so. I simply plug a back up HDD into the 3.5" hot swap bay in my computer, set Macrium Reflect to clone the main drive, then walk away. That way, I don't have to keep track of what files in what folders need backing up (a nightmare since the changed or new files are distributed across the drive). When that clone is completed, I plug in the second backup drive into the swap bay and repeat the process. I don't even have to do it on the same day although I prefer they be as close to each other as possible. Cloning is fast and easy to implement, is reliable, the data is easily accessed, and it requires no effort on my part during the process.
On the other hand, once I start putting my videos onto my computer, keeping track of new additions to be backed up will be easy so I will back them up by copying the new additions to the backup HDDs as I add them to the video drive (again, my term since I will use HDDs in my computer that are dedicated to just that purpose to save my videos to). I'll keep new additions in a temporary folder on my main HDD until a video drive in my computer and all three backup HDDs have received a copy (one back up HDD is kept offsite but gets swapped out at least once a month), then the temporary folder can be emptied. Carbonite, by default, will not upload large files, such as movies, unless manually instructed to (it takes all of three mouse clicks to do so), so I will only tell Carbonite to backup only the video saved to a video drive, not the copy in the temporary folder.
As stated before, I use three HDDs to back up each HDD I have in use. Two are stored locally for convenience in updating and recovery. One is kept offsite to avoid it being lost should a disaster take out my originals and my local backups. Since the offsite backup will be incomplete due to it not being updated as frequently as the local backups, I can use Carbonite to recover the data that is missing from the offsite backup. Since Carbonite is allowed to backup new and changed data 24/7, it also can fill the gap between local backups. I can also access my data from Carbonite from another computer, such as my notebook when I'm out of town (safer and more reliable than accessing my computer directly over the internet). However, I would really hate to have to recover all my data from online due to the time it would take to do so (hence, the offsite backup HDD). Still, if something really catastrophic were to happen, such as a meteor strike that takes out my home and my credit union six miles away while I'm lucky enough to be out of town, it is an option that will be available to me.
Reasons I've decided against data in a home server instead of keeping all my data inside my computer include the expense of the server itself, the amount of space it would take up (I just don't have room for a second box), and the difficulty of backing up large volumes (the only solution I can think of would be multiple servers which are too large to put in a safe deposit box). It is far more convenient and faster for me to keep all my data in my computer on discrete HDDs (as opposed to a RAID), then use matching discrete HDDs to put the backups on (the backup HDDs are easily stored in a dresser drawer). I don't need the assurance of uninterrupted operation a RAID would provide (the primary reason for a RAID, other than RAID 0). Having a data HDD die on me would cause an inconvenient interruption but one that can be easily and fairly quickly recovered from (restoring the system drive would take much longer but I have my notebook to keep me going until a replacement SSD can be obtained) and I can get to my data by using the backup HDDs in a dock), unlike a business that would suffer severe financial loss should data become temporarily inaccessible.
) use massive servers to store their data and additional servers in different locations to back that data up. Each location has backup power sources to avoid loss from loss of the power grid. If a location loses data to a disaster, the other locations will still have it. I suspect the different locations operate like massive RAID 10s, 50s, 60s, or something similar; each location uses some kind of RAID (other than just 0) and that RAID is mirrored by the other locations.