There were two different ways to preview compositions before (play button and RAM preview button which could also be invoked with spacebar and 0 on the number pad respectively).
Play button (or spacebar) would simply start trying to play the composition. Since AE is not a realtime video editor, this would be a slow playback as it rendered frames. If you happened to have the "green line" above a frame (indicating that it had previously rendered that frame), it would play back in real time though.
Pressing the RAM preview button (or 0 on the number pad) would begin rendering frames which would then play back, in real time once the rendering had finished.
Most professionals never used the spacebar method to play back because it wouldn't play in real time (and it wouldn't play with audio). So the spacebar was pretty wasted. If you had a laptop that didn't have a number pad, for example, you couldn't invoke a decent preview without having to click the button. Most pros like using keyboard commands! Also, new users would press the spacebar expecting AE to behave like a video editing program (which AE most certainly is not) and would be disappointed with how it would work. They'd come posting to the forums about how "After Effects preview isn't working" but it's really that it wasn't behaving the way they expected (even though it was behaving as it was designed).
So, when the Adobe After Effects team started working to rebuild After Effects' internal architecture, they decided to change how previews work. New users, pro users, and everyone in between can now preview a bit more reasonably (assuming AE is working properly...) And, the preview system can now be tweaked for how you like to work.
This page explains the new previewing system in AE: all about previews in After Effects CC 2015 (13.5)
There is supposed to be an update for AE coming "at the end of the month" (so, probably today) that tweaks a bit how the preview behaves. Some details here: What’s new and changed in the upcoming update to After Effects CC 2015