Each environment carries one overall state, shown on its card on the Environments page and again under Queue Progress on the Queue Overview page.

Figure 1. The Environments page showing one card per connected environment with its idle state, record count, queue and delete controls.
Most states need nothing from you. Three of them do.
Nothing to do
State What it means Idle There is no work to do. The environment starts again by itself at its next scheduled slot, shown as Idle until and a time. Processing The queue is running normally. If a chunk has failed you will also see a failed count. Building queue The batch is still being prepared. Wait a few seconds. Throttled Dynamics 365 has slowed EaseLog down to protect itself. Wait. It continues on its own once the limit clears. Waiting for slot The environment is outside its working hours. It starts at the next one.Idle and Waiting for slot look similar and are not the same. Idle means there is nothing to fetch. Waiting for slot means there is work waiting but the schedule has not opened yet. Neither is a fault.
Building queue appears right after you connect an environment, while EaseLog works out what to fetch. It lasts seconds:

Figure 2. Queue Overview immediately after connecting, with the environment in Building queue and a banner explaining that chunks will appear shortly.
Processing shows a live counter beside the badge, so you can watch the work move:

Figure 3. The environment in the Processing state, with a live counter beside the state badge.
Needs your attention
State What it means What to do Error Either the environment settings are wrong, or failed chunks have been left behind. If the connection is at fault, correct the organisation URL and credentials on the Connection tab of Edit Environment. If the connection is fine, open Queue Overview and select Retry All. Storage full The storage allocation for this environment is full. Clear older data, or raise the limit. Paused Somebody paused the batch by hand. It will not restart on its own. Resume it when you are ready. See Pausing and Resuming a Sync.Paused is worth knowing about, because it is the one state that never clears by itself. If an environment has been quiet for longer than you expect, check whether it is paused before looking anywhere else.
Widening the working hours
If Waiting for slot appears more often than you would like, the environment is being given too narrow a window to work in. Change it on the Schedule tab of Edit Environment. See Changing the Sync Schedule.
Note
These describe the environment as a whole. Individual chunks inside the queue carry their own separate statuses. See Queue States: What Each One Means.