From the manual:
A string of characters used as the seed for random number generation. The same seed will always provide the same sequence of numbers. An empty string (the default) will use a random seed, ensuring the sequence of numbers is different every time.The seed is effectively a key for ensuring you produce the same random number sequence each time - this is useful if you want to allow users to replay/reload procedurally-generated content, for example.
A permutation is the number of ways in which members of a set can be arranged, e.g. the letters ABC have 6 permutations: ABC ACB BAC BCA CAB CBA. In Advance Random you can create a random permutation table:
Create permutation table
Generate a randomly ordered sequence of numbers. Length is how many numbers to generate, and Offset is the first number in the sequence. For example a length of 3 with an offset of 1 will generate the numbers 1, 2 and 3, and then randomly shuffle them.
A threshold is usually a value that if exceeded will trigger an action. From Black Hornet's description of the BHTsmartrandom plugin:
A Threshold value lets you configure how the cycle repeats when all of the numbers are used, and the sequence needs to continue/cycle. A Threshold=0 will completely ignore the previous sequence, so the numbers will be random within the same range again, but it is possible that the last number of the sequence may be the same as the first of the next. For example; 2,5,4,1,3 could be followed by 3,1,4,2,5. The value 3 will repeat because the sequence must be regenerated and no logic is applied to test the last value of the last sequence. A Threshold=1, would guarantee that the first number of the next sequence would not be a 3, so there would not be a repeat immediately when the sequence restarts. Care is still required not to abuse the Threshold, as if it is too large (that is, greater than half the range), it is impossible to guarantee not repeating the same values.
Hope that helps! :-)