How to interpret Berlekamp-Massey algorithm?
Too long for a comment.
The Berlekamp Massey algorithm is a tour de force. It has the names of two Shannon award (top information/coding theory award for lifetime contributions) recipients attached and it is quite subtle.
The step you point to is a way of correcting the discrepancy between the sequence the current polynomial would generate and the actual sequence by modifying the polynomial.
Dilip Sarwate has a nice answer on this with somewhat different notation.
Berlekamp-Massey to construct minimal LFSR
The textbooks by Richard Blahut also explain the BM algorithm. The one called “Fast algorithms..” may be the most detailed.