Does 伊 have any special meaning?

there are some useful meanings of it:

1. means her/him.(usually describe as female)

薛蟠因伊倔强，将酒照脸泼去。——《红楼梦》
伊：the person mentioned above.

2. means something far from us.

所谓伊人，在水一方。——《蒹葭》
伊人: my sweetheart.

3. means somebody that you're talking with.

勿学汝兄，汝兄自不如伊。——《世说新语》
伊: you.

4. surname

In Taiwan, according to dictionary owned by Ministry of Education.

伊 means:

第三人稱代名詞，相當於「彼」、「他」。

(Third person pronoun same as 彼, 他(him).)

第二人稱代名詞，相當於「你」。

(Second person pronoun same as 你(you).)

表示肯定，相當於「是」。

(Use to denote affirmation same as 是.)

發語詞，無義。

(Words used to begin talking, no meaning.)

文言助詞，表示「剛剛」的意思。

(助詞 of Classic Mandarin used to express just(there was not much time passed only a little time passed.))

姓。

(Surname.)

伊 was used as 3rd person reference in ancient written Chinese.

In the beginning, it is equivalent to 他. But later on when Western books are translated into Chinese, sometimes "he" and "she" are confusing. The translator 郭赞生 suggested in his translation of a grammar book《文法初阶》that "he" should be translated as 他 and "she" translated as 伊. This is also guidance for original writings. The most famous literature that adopted this idea is from 鲁迅.

But later on, 刘半农（some say 钱玄同) introduced the character 她 which is used now in modern Chinese. The advantage of 她 over 伊 is that Chinese spoken language do not have a different pronunciation for different genders, so it is better to have the same pronunciation for all three 他 / 她 / 它, even though they are written down as different characters.

As a result, even though 伊 is not used now, it is still female related.

Reference: http://news.sina.com.cn/o/2005-07-26/04596526559s.shtml?from=wap

Generally, "伊" means he/she.

There is such an ancient poem "所谓伊人，在水一方", which means "My sweetheart, she is far away". In this sentence, "伊人" means "that lady". It is often used to represent the lady you admire or love.