Aayushi is a feminine given name in wide use across India. It is built on the Sanskrit noun āyus, which denotes life, vital force, and lifespan; the name is commonly read as a blessing — may she live long. Variants and relatives include Ayushi, Aayush, and Ayush, all drawing on the same root.
Personal names like this frequently become domain names, registered by the name-bearer or by family members for blogs, portfolios, or email. Adding the English article 'the,' as in theaayushi.com, is a common way to secure an available variant when the plain name is taken. None of this identifies the specific registrant of this domain; it simply describes the naming pattern the address fits.