Integration Status is the ultimate toggle for your Sync to start it and stop it.
To turn off your Sync, you will need to wait for the current sync run to finish, and then switch the Integration Status to OFF. If you do not wait for the check mark in Recent Activity to confirm that there is no sync running, you may accidentally simply pause the running sync and the next time you turn it back on it will pick up where it left off.
How to determine if your sync is running
To turn on your Sync, switch the toggle back to ON and you will be presented with a few options.
Sync Future Changes Only
Essentially this is simply catching us back up in time and as we iterate through the changes we missed while Sync was OFF, but we will not push any of the changes we see along the way. This is often referred to as a "Read-Only Full Sync"
Sync Past and Future Changes
As with the Read-Only Full Sync, we will catch ourselves back up in time, reading through changes in your connectors and while doing so we will sync the changes we recognize. This is the most common option chosen when you've had your sync turned off for some time and want to get it running again. This is often referred to as a "Read-Write Full Sync" or simply a "Full Sync".
The Advanced menu gives you the ability to change the Custom Sync Delay, and to add the condition of a Reset to your Sync.
A Reset Sync is simply a Full Sync but prior to starting, we delete all of our cached data. This means we are reading your records in as if for the first time to clear out any data we should no longer have saved.
The most common use case for a Reset Sync (Read-Only or Read-Write) is if you need to delete a large number of records from your connectors. You would want to first turn the Integration Status OFF (after waiting for a break between syncs), then delete the records, then start a Reset Sync by selecting Sync Past and Future Changes, opening the advanced menu, and selecting Reset Sync. More details on that can be found in the support article HOW TO: Reset Your Sync and Start from Scratch.