i believe that your expectations can be viewed as two things .
the first is to let many machines check their users against one central server , so we don't have to create a duplicate account and a credential on each client machine before logging in if we have already have this on the central server . a term describing such systems is single-sign-on . though a wikipedia artical of this title covers broader matters including openid and other web based services . ( i keep seeing sayings that authentication and authorisation are two different issues but personally don't quite understand . )
the second is to access many networked data as if the data are on the local machine , but are synchorised when we are walking from one client machine to another . we may call this behavior "roaming home directory" or "roaming profile" .
so for the single-sign-on problem windows deploys domains . there are implementations on unix systems to interoperate with windows domains . one implementation is samba . with samba installed a unix system can join a windows domain or set up and become controller of a windows domain . there are other single-sign-on solution for unix . i am not familiar with those technologies , but i believe this serverfault answer have good explanations , and also discusses about roaming home directories .
for roaming directories , the windows roaming profiles solution is in detail described in this article from samba , the article also have instructions configuring unix machines to visit or host windows roaming profiles . there is an abundance of other unix solutions for roaming directories . basically we can just adopt any networked filesystem like the nfs , the windows cifs , the 9p of plan9 , or the amazon s3 , then write some small automation to make a mount(2)(8) happen on login . maybe some locking is favourable for avoiding writes on a same file from multiple places . we may further come up with some local cache .
in my own experience i have a small handful of machines and don't usually access them across an internet so i just make a same account name and passphrase locally on each machine . and i use sshfs(1) to push and pull directories and files across machines .