1. The first process to run after the system boots and always has a process id of 1. It is responsible for starting the system in single user mode or spawning a shell to read the startup files. It opens ports that are designated as login ports and spawns getty processes for each on. From Linux Guide @FirstLinux

2. The first process to run immediately after the operating system loads. It starts the system in single-user mode or spawns a shell to read the startup files, and opens ports designated as login ports. From I-gloss

3. 'init' process is the first user level process started by the kernel. init has many important duties, such as starting getty (so that users can log in), implementing run levels, and taking care of orphaned processes. This chapter explains how init is configured and how you can make use of the different run levels. init is one of those programs that are absolutely essential to the operation of a Linux system, but that you still can mostly ignore. Usually, you only need to worry about init if you hook up serial terminals, dial-in (not dial-out) modems, or if you want to change the default run level. When the kernel has started (has been loaded into memory, has started running, and has initialized all device drivers and data structures and such), it finishes its own part of the boot process by starting a user level program, init. Thus, init is always the first process (its process number is always 1). The kernel looks for init in a few locations that have been historically used for it, but the proper location for it is /sbin/init. If the kernel can't find init, it tries to run /bin/sh, and if that also fails, the startup of the system fails. When init starts, it completes the boot process by doing a number of administrative tasks, such as checking filesystems, cleaning up /tmp, starting various services, and starting a getty for each terminal and virtual console where users should be able to log in. After the system is properly up, init restarts getty for each terminal after a user has logged out (so that the next user can log in). init also adopts orphan processes: when a process starts a child process and dies before its child, the child immediately becomes a child of init. This is important for various technical reasons, but it is good to know it, since it makes it easier to understand process lists and process tree graphs. init itself is not allowed to die. You can't kill init even with SIGKILL. There are a few variants of init available. Most Linux distributions use sysvinit (written by Miquel van Smoorenburg), which is based on the System V init design. The BSD versions of Unix have a different init. The primary difference is run levels: System V has them, BSD doesn't. From Linux Administrator's Guide

4. process control initialization From whatis