Inspirational character is anyone who inspires others... And yes, that sounds like I am messing with you, but actually what I am saying is that you are thinking about it upside down.
Do not think about what makes a character inspirational. Instead create issues and conflicts for other characters that require some inspiration. Then have the "inspirational character" provide that extra cue by his own example. Do that several times along the story so that it becomes a pattern and you have successfully created an inspirational character.
And yes being an inspirational character is somewhat dependent on circumstances. It can be seen as being a bit ahead of your time compared to your peers. Alternately you can be in some way more mature than your peers.
Generally there is also a factor of not being afraid to be different so that others can easily learn from your example. So an inspirational character would generally at least look like being confident. People usually pay more attention to confident people as well. But it is possible to be only confident in silent or partial fashion. You do can be insecure about some things and inspirational about others. And the confidence can be in form of simple understated competence.
An example would be a mother who tirelessly works to raise her children. No glamour, no prestige, just simple emotional maturity of really understanding she loves her children and putting them first is not really giving up anything.