Hey Lalida,
Program Statuses are what you set up for your Channels. It is how they flow through the Program. You need to designate at least one status as a success (Marketo won't let you approve without it). This is crucial for mutlti-touch reporting, this is how Program influence is attributed.
To your specific question, for those who have their status changed to Member, it means they either exhibited a behavior, or were part of a user defined behavior, that was needed to gain membership to the Program. In your example, it appears that to be a member of the Program, all they had to do was be sent an email, which is pretty typical of Email Programs.
The second part of your example is interesting. Could you provide a screenshot? My guess would be that there is a trigger campaign looking for Leads who were sent the email. When they were sent the email, they are added to a list and have their status updated to Sent. This way, you have more control over who becomes a member of the Program. For example, if you only want folks who actually received the email (Email Delivered), then you could set up trigger campaigns to look for the email being delivered, then once they are, you can pull them in to the Program.
Hope that helps!