My attempt as learner:

What does love mean ?

Love means longing.

Love means to love.

Love means to love very much.

Love means to love unconditionally.

Love means my feeling of love to you.

Love means to feel you in my heart.

Love means to mention your name without forgetting it. (not sure about this part)

Thank you..You are not sure of the last part??

Yes, I´m not sure about the last sentence - dictionary says that word "Zikretmek" means "to mention", however there are also another meanings of it (like "chant") and I wasn´t sure how this sentence should be translated. Maybe someone more advanced can help here with this sentence ?

zikretmek also means to say something (especially the word Allah) again and again. 

Zikretmek means to glorify and praise Almighty Allah usually verbally , you will notice beads in the beautiful Turkish Mosques.

tomac´s translation is correct...zikretmek here means "to mention"

"karþýlýksýz" mean "unconditionally" in English as its usage? "unconditionally" means "þartsýz" but karþýlýksýz is "unrequited" or "unanswered"

Thank you all for your comments! I had a problem with the sentence that caliptrix mentioned - I had no idea how to translate "Karþýlýksýz Sevmek" concisely, but I found this translation in tureng.com:

and decided to use it in my attempt. Good point about it, in my opinion, is that it is short (like the original sentence), however, as caliptrix has written, the meaning is not quite the same.

I have another two ideas: the first one is short too, but I´m not sure if it is correct sentence in English? Can someone help me and tell if it is correct?

Love means to love without an answer.

And the second idea (with a small variation) is unfortunately longer, but I guess that it is correct:

Love means to love even when it is unrequited.

Love means to love even when the feeling is unrequited.

My thoughts:

Love means to love without an answer.

In my opinion this would be better as:

Love means to love without (needing) a response. 

Love means to love even when it is unrequited. Sounds fine to me.

Love means to love even when the affection is unrequited.

In my opinion it is better to say it rather than change love to feeling (or affection) as it keeps the original meaning

Unrequited means not reciprocated or not returned.