Welcome, sokatron!

sundialsvc4 did an excellent(!) job addressing the concept of a reference to assist you with resolving your array issue.

Although unsolicited--and I apologize in advance if I've confused the issue here--consider the following which doesn't use the C-stype for loop (e.g., for ($x=0; $x<$size; $x++)):

#!/usr/bin/perl
use strict;
use warnings;

print "How many replicates? ";
chomp( my $antal = <> );
print "How many Samples? ";
chomp( my $size = <> );

my @a; # Consider a more descriptive name for this array.

for my $tim ( 0 .. $size - 1 ) { #For each Sample the number of replic
+ates are entered
    for my $tam ( 0 .. $antal - 1 ) { #For each replicate in the sampl
+e a value is added
        print 'Enter replicate value '
          . ( $tam + 1 )
          . ' for sample '
          . ( $tim + 1 ) . ': ';
          
        chomp( my $repValue = <> );
        
        $a[$tim][$tam] = $repValue;
        #push @{ $a[$tim] }, $repValue; # This notation can be used, t
+oo.  Is there a "Golden Ticket" here?
    }
    
    print "\n";
}

for my $tim ( 0 .. $size - 1 ) { #For printing and checking all values
    print 'Replicates of sample ' . ( $tim + 1 ) . "\n\n";
    
    for my $tam ( 0 .. $antal - 1 ) {
        print 'Replicate ' . ( $tam + 1 ) . " value is: $a[$tim][$tam]
+\n";
    }
    
    print "\n";
}
[download]

Hope this is helpful.