A domain name backorder means paying a domain registry to monitor an existing domain name that someone else owns, and if it becomes available the registry attempts to register it for you.
There are many such services, and in fact most domain registrars provide it.
However it's not 100% successful. Particularly popular domain names may be backordered by many people, so when it becomes available several automated systems may be attempting to register it at the same time, but only one will succeed.
The current owner of the domain name is not notified, but check the fine print of the backorder services you evaluate.
Keep in mind that if someone else backorders the same domain, on the same registrar, you suddenly have a conflict - which of you two will the registrar actually attempt to register the domain name for? The registrar may not tell you that the domain name you've backordered has also been backordered by other customers of theirs. You might consider asking them how they manage such situations.
Read the backorder terms. In general if you backorder the domain and the attempt is successful, then you own the domain just as though you had registered it yourself, and you can use whatever hosting provider you choose.
If you backorder through a domain registration service that only bundles domains with hosting packages, then you may be stuck with them for hosting.
Whether you should buy domain names and hosting from the same service is a separate question entirely...