Is this necessary my $b = $b[$i];?

Strictly necessary for function, no. Quicker and clearer, yes.

Like a bookmark (or locking a tab) for a page you reference frequently. Perl is not so good as statically compiled languages at sub-expression elimination.

He added

<#> gv[*b] s                      # my $b = $b[$i];
<1> rv2av sKR/1
<0> padsv[$i:2,4] s
<2> aelem sK/2
<0> padsv[$b:3,4] sRM*/LVINTRO
<2> sassign vKS/2
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in order to replace a large number of

<#> gv[*b] s                      # $b[$i]
<1> rv2av sKR/1
<0> padsv[$i:2,3] s
<2> aelem sK/2
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with

<0> padsv[$b:3,4] s               # $b
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Assuming each of these ops take roughly the same amount of time to execute, this adds up. Basically,

my $b = $b[$i]; ... $b ... $b ... $b    # 6 + 1*3 = 9 ops
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is faster than

$b[$i] ...  $b[$i]  ... $b[$i];         # 0 + 4*3 = 12 ops
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Since his code looks up $b[i] 4 to 8 times (depending on the value of $b[$i]), this saves 6 to 18 ops. Per loop pass!