Twitter has now brought the real time tweet updates feature to the user's home page. From now on you will be able to see a notification about the new number of tweets that may have arrived from your peers. For all those who do not know, this feature has already existed on Twitter search.
As you can see below, the screenshot shows that six new tweets have arrived since you updated the home page last. All you need to do is just click on this link that shows the number of tweets and the page will reload will all new tweets updates.
Image Courtesy: Real Time Twitter Logo - acm.org