I don't think user4358's explanation is correct. A trailing LIT Sell Order adjusts downwards, i.e. if you place the order with an Aux price (in TWS it's trigger price) of 105.00 and a trailing amount of 6.00 then, assuming the ask is 100.00, TWS will add the trailing amount to the ask price and if it's less than the trigger price it will adjust.
So in my example, if the market (ask) goes straight up to 105.00, nothing will be adjusted, the trigger is touched and the limit order will be placed (see below).
If on the the other hand the market goes down to 99.00 then
trlng amt + ask is 105.00, if it goes further down to 98.00 then the trigger price will be adjusted to 104.00 (because it's less than the current trigger), and so on.
For the LIT part you have either an absolute limit price you can enter, or you have an offset limit which will be subtracted from the trigger price, in which case it is adjusted as well.
So back to my example, the trigger is now 104.00 and the limit offset is say 1.00, so my limit order would be placed at 103.00 if the ask ever touches 104.00, and that in turn is only visible if the bid touches 103.00 (because it's limit-if-touched).
For a buy just use the same explanation with some swapped roles, the trigger price adjust upwards when the trailing amount plus bid is larger than the current trigger, and the limit offset will be added to the trigger price.
Also quite succinct and worth having a look at: http://www.interactivebrokers.com/en/trading/orders/trailingLimitTouched.php
Guesswork, highly subjective
As for why this might be good, well, you have to believe in momentum strategies, i.e. a market that goes down, will continue to go down, if you believe that and you believe in mean reversion as well, then a trailing limit order can assist you in not buying/selling impulsively, but closer to the mean. I've never used it that way though.
What I have done, even just now to get the explanation right, is to place trailing buy and sell orders simultaneously. You will find that you can just go in with coarse estimates and because the adjustments will go towards each other, you will end up with a narrowing band of trigger prices (as opposed to trailing stop orders which will give you a widening band of trigger prices). If you believe in overshooting and equilibria then this can be one easy way to profit from it. I've just sold EURUSD for 1.26420 and bought it back at 1.26380 with a trailing amount of 5pips and a limit offset of 2pips within the time of writing this.