Besides speed, a good browser should focus and offer safety because there are many threats on Internet, fake pages (phishing) to steal personal information such as credit card numbers, pop-ups which may install viruses, malware (viruses) hidden in images or downloadable file and so on.
A good web browser should load web pages quickly and should be able to work seamlessly when there are multiple tabs in the same time, because these days we use often different services such as e-mail, social networks, entertainment sites in the same time and we like to receive real time updates about new things. Most important things are speed, safety and the easy use.