What is the holding current on a triac?
To answer this, consider the simpler to understand SCR instead of a triac.  A triac is sortof two SCRs back to back and therefore can pass current in both directions.  A SCR only works one way but has the same issue of holding current.

Here is a equivalent circuit of a SCR:



SCRs are actually built as one integrated device, but you can conceptualize them as two transistors like this.  In fact, you can even make a scr from a NPN and PNP transistor like this if you just want to experiment.

Look at this circuit carefully and see how it works.  If somehow a little current were to flow thru one of the transistors, let's say Q1, that causes base current to flow thru Q2, which causes even larger base current thru Q1, which then turns on Q2 even more, etc.  Once a little current starts flowing, this circuit latches on.

Now imagine current is flowing and the gate is left open.  As long as the current continues, the circuit acts like a switch in the on state.  However, below some level of current, the cascading amplifying effect can't be sustained anymore, and the circuit switches off.  This minimum level of current so that the device is guaranteed to stay on is the minimum holding current.

This circuit only works with current flowing in one direction whereas triacs work in both directions, but the concept of the minimum current to keep the device on is the same.