All the standard items as mentioned above, needed for a complete change--if necessary. However, I would much rather patch-up and contain a leak, if possible, so my kit is highly geared for that. So far, I have never had to change away from home.
With my standard change items, I also carry in my kit:
A small empty spray bottle to be able to fill it up at the sink and have a water source in a bathroom stall.
Two regular feminine napkins [longs] which can be placed around or on either side of the leaking wafer to sop up and help contain a leak. If needed, the adhesive will sick to underwear to hold the pad in place.
Waterproof tape.
A small spray mouthwash or breath freshener to cover odor.
A pen-sized hand sanitizer spray.
A few round make-up removal pads which I use in place of pieces of toilet paper.