It's someone like my modest persona.

In British English it is used a euphemism for "obnoxious". Example: "My new boss is not evil, but let's just say that she has a big personality." [she is annoying]

It means their personality characteristics are unmistakable. They have a definite presence. When you meet such a person, you remember what they are like because their characteristics make such a strong impression. In other words, they don't just have a personality, they have a PERSONALITY!

Someone who is outgoing and sociable.

A big personality is usually used to describe someone who is most likely an extrovert, outgoing, loud, confident in his/her beliefs, can easily express themselves etc... We use this phrase when we want to say that the personality of someone is expansive, and not restricted. I hope that helped! Feel free to checkout the great reviews from my wonderful students. Hope to hear from you soon! 😄👍📚🎯