Slightly off topic but is איש not used in modern hebrew to say 'man'?
Hebrew does not have an indefinite article. In other words, there is no word for "a".
"woman" or "a woman" is אישה and women, an irregular plural, is נשים
What is the point of having the aleph letter if it is useless most of the time?
Its a glottal stop. You kind of just stop or take a break in the middle of a word and thats its pronunciation. Its not useless, youre just not used to it. if you know the arab alphabet their ا has the same sound(or rather lack of sound).
One helpful way I was taught to think about aleph when I began learning Hebrew is as a way to mark syllables which begin with vowel sounds. It's not a technical explanation, which Skulte91 already gave, but it does help think about what use the letter has. Think about how many words and syllables in English start with vowels.