I’m learning the solo for Let it be but i noticed in the chord progression, during the brake, there is the sequence: Bb Am G
The song is in the key of C major and i know that you don’t have to use only the chords in C major and I’m not questioning the use of the Bb. However i want to understand what makes it work.
And from this i could ask how do i know which “out of the key chords” sound good in combination with the respective key?
This would be a very good place to start. 
I presume you’re looking at something like this on UG?
Although this gives F/A not Am.
Follow the lowest notes of the chords.
F → E → D → C → Bb → A → G → F
That is just a superbly satisfying walking bass line.
And each chord is fleeting.
This is on a piano where inversions / slash chords are just a finger movement away.
I do not know what spread of notes are played on the keyboard through this passage. I will write all chords as triads and the slash chords as 1st inversion triads because the bass notes are the 3rds.
F = F A C
C / E = E G C
Dm7 = D F A C
C = C E G
Bb = Bb F D
F / A = A C F
G = G B D
F = F A C
C = C E G
The Bb is an out of key chord. It can be termed a borrowed chord. It can be named as a bVII which is a commonly borrowed chord.
Look out for bVII in the examples with the topic Toby linked.
It works because it sounds good.
This is all about ‘voice leading’. The voice leading is strongest in the bass notes but evident elsewhere in the chord movement.