According to emerging reports, there has been a major flaw found in the web browser that comes as standard in millions of Android devices. If exploited, this vulnerability would allow an attacker to view other websites that the browser may also currently be accessing. In other words, if you had your webmail open in one tab, and a page exploiting this bug in another, the attacker could read through your emails, and even send an email from your account as though it came from you.
The browser in question is called simply "Browser". This is the default (or "stock") browser that comes with most older versions of Android. Google no longer support this browser and have since replaced it with Chrome by default. However, millions of Android devices will still be running an older version (Prior to 4.4, or 'Kitkat') as phone providers tend to only support Android updates for a short time. This means this bug will never be fixed on these devices.
Therefore, if you are still currently using the "Browser" app as a matter of course, our advice would be to stop using it immediately. Instead, go to the Play store and install an alternative web browsing app such as "Chrome" or "Firefox". Installing one of these browsers has the added advantage that they will continue receiving updates to keep your browsing secure even though Android itself isn't being updated.