The importance of a letter 'h'

I was looking up the ages of cabinet members last night and made a spelling mistake. For a moment I was reading that Teresa May was 'Teresa May (born Teresa Betteridge, December 15 1967, Epsom, Surrey) is an English glamour model. In addition to films, May has appeared in numerous ...' was surprisingly younger than me and had an alternative career to politics then I realised that I had omitted an 'h'. Theresa May however is described thus 'Theresa Mary May (née Brasier, 1 October 1956 in Eastbourne, Sussex) is the Conservative Home Secretary of the United Kingdom. She is one of the most senior ...'

The letter 'h' is an important one, isn't it?