A PvE bracket has room for 1000 players. Once it is full a new bracket is started. This is the "flip". The less players are in the bracket when you enter, the more of an edge you have since you'll be able to rack up more Points by playing optimally and thus you'll get better placement.
Bracket sniping basically means waiting until the end of the event, enter a fresh bracket, and getting good placement rewards with very Little work.
Progression is a good goal, Bob, so I'm assuming you are doing 4 clears of each node for full progression. But sub placement can also be an easy way to make extra HP. In SCL 8, a top 50 sub finish is worth 100HP. Placing 51st gets you zero HP. If you join a later, less competitive bracket, you could get a top 50 finish with the same 4 clears of each node that might only get you a top 100 finish in an earlier, more competitive bracket. And because you stay with the same group throughout each sub in the event, this can pay off by making things easier for every single sub. That's a potential 100 extra HP per day for the same amount of play, just by joining the event a bit later on the first day. Not a bad deal.
Take a look in the event sub forum - there is normally a post about bracket sizes for each pve. This used to be done by comments posted as people entered brackets or saw them fill, now it's linked to a spreadsheet updated from Line communication.https://forums.d3go.com/discussion/66786/webbed-wonder-2017-08-03-to-2017-08-06-bracket-size#latest
Bracket sniping does also apply for PvP, same concept - trying to hit high placement by taking a "fresh slice"... used especially frequently on new character releases (like the Weapon Tex-Mex that just finished - top placement earns another Mockingbird cover)