~ does the string concatenation. The dot in Perl 6 is now used for dealing with methods; thus, a new operator for the string concatenation was required. The tilde was a good candidate because it is also used in other string-related operators in Perl 6.
say "a" ~ "b"; # ab
If necessary, the operator converts its operands to the string type.
say "N" ~ 1; # N1 say 4 ~ 2; # 42