There are two ways LeadSimple tracks emails.
If your email account is not connected, LeadSimple provides a unique tracked email address for every lead in your account. When you email the lead through that address, the email is forwarded to the prospect as you would expect, but it is also logged in your account for future reference. The prospect will see your email address in the from field when they receive the email. But when they reply, their email will be directed to another tracked email address which routes back to you through LeadSimple, logging the email in the conversation history in the process.
If you connect your email account to LeadSimple (see the article called "Connecting your Email Account"), the system will search your email inbox for any emails sent to or from the email addresses of leads in LeadSimple. All those emails will be imported into the record of the lead they're associated with. This allows you to email leads from Gmail, for example, like you're used to and at the same time have those emails be tracked in LeadSimple.
Note that setting your pipeline or process tracking to "Broad" or "Relevant" will also affect how emails are tracked. More on this here.
In either of these cases, LeadSimple will track the number of times a given email has been opened by leads. This activity is tracked in that lead's record in the system.