At the end of Revolutions, the machines took Neo's body and hooked him back up while making changes (wiping his memory like a dirty install of Windows) and then rebooted him back into the Matrix. The therapist that Neo is seeing is a AI program monitoring Neo to make sure he doesn't recover (notice the blue glasses matching the pill). He aimlessly roams around getting older and bumps into Trinity at a coffee shop and a moment happens (his love for Trinity is immeasurable) and is then later found out that she is just a program as you can see from a scene her face is just Matrix code. The new team has figured out Neo is alive (with help of Sati telling the new team) that Neo is jacked into the Matrix and they launch a recovery team to go in to perform a Data Recovery of his mind (similar to a data recovery process of a hard drive in real life) hence the screen you see showing the old footage of Neo being jacked in for the first time. As they are jacked into his mind (also take note the computers with matrix code on the monitors, and a target symbol of when his 6th version exited the Matrix) after taking the red pill (which cuts the monitor software to Neo) wears off and the system comes after Neo and team. The team was able to recovery small bit of data and Neo wakes up and gets his powers back but not all of them because the data was fragmented. This also explains he can push things, stop bullets etc. Another note the trailer shows is the representation of everyone on their mobile phones which represents everyone connected to the hivemind (the matrix AI) and will play a vital role of the system turning against the new team and Neo.