If a character's dialogue is:
'I love porridge. Aunt Alice sent us a postcard - did you see it?'
then there has to be a pause or beat between the two sentences:
'I love porridge.' (BEAT) 'Aunt Alice sent us a postcard - did you see it?'
because there is a change of direction in the character's thinking from the first sentence to the second, from porridge to the postcard.
On stage the actor would pause or perform some action between the two sentences. When you got your script for the first time you'd go through marking the beats, working out what the thinking was behind the words. (I acted in a Pinter play once and we spent some time working out how many beats there were to stage directions such as pause (2 beats), long pause (4 beats), brief silence (6 beats) etc.)
That's in acting. The word beat is used in film scripts, but it's used in the same way - to indicate a pause in dialogue. And from film the word beat has come into prose to describe the spaces between dialogue. But in prose we can't hear the characters pause, so we have to write something...
'I love porridge.' She wiped the table down. 'Aunt Alice sent us a postcard - did you see it?'
'I love porridge.' She looked up as the letterbox rattled. 'Aunt Alice sent us a postcard - did you see it?'
'I love porridge.' A mouse ran along the edge of the skirting board. 'Aunt Alice sent us a postcard - did you see it?'
Every time your character changes direction in their thoughts there should be a beat, unless you want to indicate a character whose thoughts just rattle through their head - for example, Miss Bates' long speeches in Jane Austen's Emma.