How much website traffic a shared hosting server or shared hosting plan can handle depends on the type of website you have.
A website that only uses html could get 30,000 daily unique website visitors and the shared hosting server might be able to handle that just fine.
But take a website that runs on php and has a mysql database such as a forum or a wordpress website then the amount of visitors the shared hosting account can handle will drop.
A website using php and a mysql database can probably stay on a shared hosting account while getting 3,000 daily unique's.
Once you get 3,000 daily unique visitors to a database driven website such as a forum or wordpress blog then you should look at moving to a vps server or a dedicated server.
With 3,000 daily unique visitors to your website you should be able to make some money off your website through Adsense or other ad networks that should provide more then enough online income to cover a vps hosting account or even a dedicated server.