Yes, it is often possible for your boss or your employer to read your email messages. Often, companies will have an email policy or a communications policy that employees have to sign. This informs them of the fact that communications and activities on the computer may be monitored.
After all, this could be a work email system to which the employer also has access. On top of that, activities that are performed on a work server or network can sometimes be monitored independently.
For instance, some software systems allow employers to monitor activity as it happens on the screen. Even if an employee was logged into their private email, such as their personal Gmail account, if they were reading those messages while their screen was being monitored, that information would still be visible to their employer.
What if you use incognito mode?
Employees may be tempted to use incognito mode or private browsing mode, believing that they are keeping their activities a secret. They may think that this gives them a greater level of privacy.
The important thing to note is that these browser modes just hide records of activity performed on the local device. For instance, the browser itself will not record a history of the sites that a person visited. But that information can still be visible to an employer, a network administrator, an internet service provider and other such entities.
In general, employees should assume that any activity they take on a work computer, or through a work email address, is going to be monitored. This can lead to some privacy concerns, and it is important for those involved to understand what legal options they have.