What am I missing

The $word* variables aren't getting assigned "an array", they are getting assigned the values from the array.

@collect = split( / /, 'This is a sentence.' );	The array on the LHS means that the assigment is in list context. Split returns a list of scalars. In list context, the elements of what's on the LHS get assigned to the values from the list on the RHS, so the @collect array is populated from the values returned by split
( $word1, $word2, $word3, $word4 ) = @collect;	The (...) on the LHS mean that the assignment is in list context Per List value constructors, the @collect array gets evaluated in list context, which results in the list (on the RHS) consisting of the elements from the @collect array The assignment then happens in list context, so the leftmost item of the list on the LHS ($word1) gets assigned the value of the leftmost item from the list on the RHS, and so on
print join( q[ ; ], ( $word1, $word2, $word3, $word4 );	=> syntax error at parv.pl line 3, near ");" but with a second ) on that line to allow it to compile: the words are given list context by the parentheses (unnecessarily, because join already gives list context) join concatenates the elements of that list, using space-semicolon-space as the separator, into a string That string is then printed.

(LHS = "Left-hand side", RHS = "Right-hand side": in these cases, relative to the assignment operator =)