Shmuel Brin's answer really covers the question as asked. However, the concept was explored and developed much further, which you can access with the Sefer כללי רש"י by seeing the points and checking the sources that it brings. It also brings there that Rashi departs more from Peshat in his pirush on Nach, because the target audience (בן חמש למקרא) is older at that point.
However, a couple of pointers to help understand it a bit better. First, what does the Rebbe mean with there are different levels of Pshat? And what does Pshat mean, exactly?
On the first, I would compare it to the introduction to Ein Yaakov from Rabbi Avraham Ben HaRambam where he says there are 5 levels to drash similarly to Pshat, there are different levels to it (I'm not saying that they correspond to those 5 levels - I'm just illustrating the concept).
So what is Pshat? As I heard from Rabbi Elimelech Tzveibel, Pshat means the understand that comes from the text without adding concepts that are not required by the text - but the totality of the text, not just a specific verse in isolation.
So according to all of that, sometimes the plain text stands on its own. Sometimes, however, the plain text doesn't work on its own. It poses unanswered questions. This is the plain text telling you you need to add a level of hagada that is in harmony with the plain text, but isn't what the plain text (פשוטו של מקרא) tells you. So Rashi adds ולאגדה המיישבת דברי המקרא.
However, there are entire areas of אגדה which would be completely unrelated to pshat. For example, Berishis Rabba describes the beginning of Vayerah as Avraham sitting in front of Gehennom (like the heat of the day) keeping all those with a Bris out. That has no relationship to what is intrinsically understood from the text, and thus has no place in Pshat.
Sometimes such an Aggada would explain problems in the text, but it is still too far away from Pshat for Rashi to include it, although he may allude to it.
