Does the emclient download the emails to system or just shows the emails on email server?
When configured with POP3, eM Client uses the local computer as the message store, so messages and embedded content will be downloaded and removed from the server.
When configured with IMAP (default), eM Client uses the server as the message store, and only keeps a synced copy of the message headers on the local computer. Additionally eM Client can be configured to download the message body including embedded content for offline use.
With the downloading of IMAP emails for offline use, could this be done for the Inbox only? That way I’m not waiting for each email to load as I go through them each day.
I don’t want to download my whole acocunt as thats way too much data when it also includes attachments.
Just the inbox 
Joel as far as i’m aware you (cannot specify) to only download the server Inbox for IMAP. You normally get all the server mail folders using an IMAP Acct. If that is not the case, someone will update this thread.
However once the IMAP email is synchronized & cached to your local computer, the previous emails actually opens very quickly depending on the speed of your computer and internet connection. As Gary says you can also configure EMClient for offline use as well.
Before version 8 beta was released there was some mention in the blog that it would support selective syncing of IMAP folders or age specified syncing. Can’t remember which, and the blog entry seems to have been removed. But I think it was age specified, so it would be possible to set a folder to sync only the past month of messages.
Either of those features would be useful to you Joel, so just keep an eye out for any developments as not all planned/promised features are present in the current beta release.
In either version 7 or 8, when set for offline mode, eM Client will download a cached copy of the complete message in the Inbox in real-time. Other folders are synced according to the schedule in Menu > Tools > Settings > General > Synchronization. So if you increase the value there, the syncing of the other folders will be less frequent. Of course when you click on one of those folders it will initiate a sync regardless of the sync interval. The download will only take place once for each message. It is not that it has to redo the download every day.