Case #1 - You are attempting to go long at 1000 LIMIT and the inside market is 1000.50 x 1001. The Chase Limit is set to 1. When the ASK moves up to 1001.50, your 1000 LIMIT order will then be adjusted to 1000.50. When the ASK moves up to 1002, your LIMIT order will then be adjusted to 1001. If the ASK moves up  again to1002.50, your LIMIT order will remain at 1001 since the amount that has already been adjusted equals the Chase Limit parameter of 1. Also, the Chase button outline will turn orange indicating you have hit your limit.

Case #2 - You see support at 1000 and the inside market is at 1002 x 1002.50. You put in a LIMIT order at 1000, check the Chase Trigger option and set the Chase Limit to 1. This means, you are willing to pay up to 1001 to get into a long position. You press the Chase button. At this time, Chase is not chasing. It will wait until the ASK is at 1000.50 before it will start chasing the ASK up. The value of this is that sometimes, you may not get filled at the support level, so instead of letting the trade get away from you, we wait to see if we get filled at 1000. Since the bid is now at our entry limit price, we hope we get filled, but it doesn't happen this time. Instead, the market starts moving back up. As soon as the ASK lifts to 1001, our LIMIT entry price will start chasing it.