One the benefits of a shared hosting account is that the operation of the server, by and large, is managed by the web host. Your website itself is still your responsibility, but pretty much everything else is up to your host. This advantage can also be a disadvantage because it means you have limited access to resources and not much decision-making power when it comes to server configuration.
The amount of flexibility you have in your shared hosting account varies from one hosting provider to the next. For example, some may give you the ability to create .htaccess files or even php.ini files to make local web server configuration adjustments. Others may lock down these features or only allow their usage on more expensive hosting packages.
SSH (Secure Shell) is one such feature that your host may or may not make available to you. The easiest way to find out is to ask before you sign up for an account. The original question, however, was whether you actually need SSH or can do just fine without it.
SSH gives you the ability to access the server’s command line. With a shared hosting account, you will have limited access to commands and will most likely be chroot jailed into your own home directory. System administrators will view any shell user as a potential security threat, so you can expect to be monitored closely.
The reality is, most web-based control panels will give you access to tools like cron jobs without needing a shell account. If you need to perform more advanced tasks and use shell commands, you should make sure you get a web host that will allow them or consider getting a low-cost VPS.