After you file

Your acceptance date can be before the official opening day because the IRS pulls a number of returns each year (always has) in test batches sometimes as early as a week before the official filing date to test all of their systems.  Many people file early hoping to be selected for this process because they think it will speed up their refund.  It won't.  Even if everything goes perfectly in the test (and it's just what it sounds like - you're being the guinea pig), your refund will still not be released until they start releasing them for everyone.  

Still being processed means exactly what it says - the IRS has your return and they're still working on it. This year lots of things are holding up processing.  It is still possible for you to get a letter of that it may finish soon.  It is impossible to guess why it is still being processed - could be that you indicated that you did (or didn't) get a stimulus payment and their records show something different, that they need to verify your identity, that they show you had a marketplace insurance plan but you didn't include information from your 1095-A, that you were required to file 8812 to get certain credits, or simply that you were randomly selected for manual review/processing - which happens to as many as one-third of all returns with refundable credits.  

@taraholly10 - it's not possible to be accepted before transmission.  This is what happens after you click on the "transmit my return now" button in TurboTax -  first it goes to the software company's server (Intuit). It sits there until the IRS pulls it to theirs (it isn't pushed, but pulled) - this is when the status changes to Transmitted.  During tax season this happens many times an hour.  Prior to official opening day it happens to randomly selected returns.  Occasionally during tax season, there is a pause.  Once the IRS pulls the return to their server, the computers do a quick check of a few specific items and decide to accept the return or reject it back to Intuit's servers.  This is when the return status changes to Accepted.  At this point, no more data is sent to Intuit (or any other software company or tax preparer - it is all up to the IRS from here on out.) 

Once it is accepted it goes into a processing queue.   Many returns sail through the processing returns in a fully automated process. For that to happen pretty much everything has to match up exactly as the IRS computers have on their end.  Mismatches can occur because of data the taxpayer has accidentally left off, because of a change to a form or tax law between the time it was sent in and the time it was accepted (this used to be unheard of, but it's becoming more common and this year it may continue to happen as changes continue to be made.)  It can even happen if an employer is simply late sending in their side of your W-2 data. 

Everything that happens after your return has been accepted happens at the IRS.  Sometimes folks at TurboTax or other users of this forum can share their experiences from the past with different scenarios but the reasons are so numerous that with a few exceptions (certain codes are very generic, but a few are very specific) there is little way to tell until you do receive a letter from the IRS explaining the delay (and if you've not reived a refund within about a month under current circumstances, it is highly likely that one is coming - and it could be weeks to months away.)