Irritability and excitability refer to two different emotions that force our body to deal with an event or situation that is causing emotional stress.
When we say someone is "irritable" this means he/she could be in a bad mood which can be brought on by illness or a situation.
For example, someone may be upset or inconvenienced when their ride is late or when someone is rude to him/her on the phone.
When we say someone is excited, we usually mean that he/she is looking forward to a pleasant event, such as an upcoming trip or spending time with family on a holiday.
Merriam-Webster Medical Dictionary describes excitable as “…capable of being activated by and reacting to stimuli: exhibiting irritability” which usually refers to living tissue or an organism but does not describe how most people outside the medical community characterize these emotions.
Let's try this. If you say someone is irritable, you usually mean that they get angry easily. As in, "My irritable sister almost bites my head off whenever I ask her a simple question!"
Someone who is excitable is just, well...easily excited! Just teasing. It means that they get really hyped up about things--not angry, just really wild and crazy about things. So you might say, "I don't understand how anyone could be as excitable as Ellen. Just say 'Hi' and her face lights up and she starts squealing like you're Justin Bieber or something. Wow."
That's a long example, but I think you get the idea, right? Hope so!