In the old patterns this thicker thread is often simply denoted by "PC" which stands for "Padding Cord".
The use of the padding cord gives the Irish crochet its distinctive 3D look.
It can be quite fiddly to work with a padding cord at first, and you have to be careful to keep it out of the way of your working thread - otherwise you can spend as much time undoing knots as working on your crochet !!
Remember that no matter how careful or delicate you are with creating your crochet the padding cord will show through in places, so where a thicker thread is required for the padding cord get one that matches the colour of your working thread. Where it isn't possible to get a thicker thread of a matching colour its best to just make up your padding cord with multiple strands of your working thread.