Most of the values¹ in
limits.conf are limits that can be set with the
ulimit shell command or the
setrlimit system call. They are properties of a process. The limits apply independently for each process. In particular, each process can have up to
nofile open files. There is no limit to the number of open files cumulated by the processes of a user.
nproc limit is a bit of a special case, in that it does sum over all the processes of a user. Nonetheless, it still applies per-process: when a process calls
fork to create a new process, the call is denied if the number of processes belonging to the process's euid is would be larger than the process's
limits.conf man page explains that the limits apply to a session. This means that all the processes in a session will all have these same limits (unless changed by one of these processes). It doesn't mean that any sum is done over the processes in a session (that's not even something that the operating system tracks — there is a notion of session, but it's finer-grained than that, for example each X11 application tends to end up in its own session). The way it works is that the login process sets itself some limits, and they are inherited by all child processes.
¹ The exceptions are
chroot, which are applied as part of the login process to deny or influence login.