Specifically, what verses in the Quran define or explain love?
This could be verses that mention romantic love, or love (deep friendship) for one's fellow man, or love (pity) for the unfortunate and poor, or one's love for (devotion to) Allah, etc.
Well you have multiple questions in single line, i might to touch the tip of the ice burg.
On love between humans. Read here and follow, but 1 thing i should make clear, love among humans is not only love of opposite sexes only for sex, love is when you for something good for someone else for the sake of humanity.
And of His Signs is that He created for you from yourselves mates that you may find tranquility in them; and He placed between you affection and mercy. [Quran 30: 21]
It is not righteousness that you turn your faces to the East or the West, but truly righteous is he who believes in Allah and the Last Day and the angels and the Book and the Prophets, and spends his money for love of Him, on the kindred and the orphans and the needy and the wayfarer and those who ask for charity, and for ransoming the captives; and who observes Prayer and pays the Zakat; and those who fulfill their promise when they have made one, and the patient in poverty and afflictions and the steadfast in time of war; it is these who have proved truthful and it is these who are the God-fearing. (Al Quran 2:178)
Allah is with those who are of service to others. (Al Quran 29:70)
“On the night of the fast it is lawful for you to have sexual relations with your wives. They are clothing/covering (libaas) for you and you for them….” (2:187)
In ahadees(Sayings of prophet peace be upon him)
"By Him in Whose Hand my soul is, you will not enter Paradise unless you believe, and you will not believe unlessyou love each other.Should I direct you to something that if you constantly did it, you wouldlove each other? Spread the greetings of peace among you." [Muslim]
“Allah will ask on the Day of Judgment: ‘Where are those who loved each other for the sake of My glory? Today, - on a day when there is no shade but mine – I shall shade them with My shade.” [Sahîh Muslim (2566)]
Hope it has something related to what you are looking for.
The Prophet Muhammad (s) said: “Be kind, for whenever kindness becomes part of something, it beautifies it. Whenever it is taken from something, it leaves it tarnished.” – Imam Bukhari’s Book of Muslim Manners.
In Arabic love can be translated to various words. The most common ones are عشق and حب and شغف. The first one does not appear in Quran. The second one is common and will be discussed below. The third one appears once in the story of Prophet Joseph.
There are two instances of love between women and men that are mentioned in Quran, one positive and one negative.
The negative one is the love of Potiphar's wife towards Prophet Joseph which is narrated extensively in the middle part of the sura Yosuf starting at verse 12:23.
The positive one is more implicit and is the story of the love between Moses and one of Jethro's daughters narrated in sura Qasas starting at verse 28:23.
There other verses which discuss love more generally, e.g. love of believers towards each other, love of God towards his creations, love of believers towards God, love of disbelievers towards worldly matter like wealth, etc. There are also verses also metaphorical verses which some have interpreted as being related to love between women and men, e.g. verse 24:35-36.
"And [it is also for] those who before them had homes [in Medina] and had adopted the faith [before the Emigrants], love those who emigrate from Mecca to them and in their hearts they feel no need for the booties granted to Emigrants though they live in dire poverty, but give Emigrants preference over themselves. And those who are delivered from covetousness, such are they who shall find deliverance". (59:9)
Mu'adh b. Jabal reported that the Messenger of Allah (ﷺ) caught his hand and said: "By Allah, I love you, Mu'adh. I give some instruction to you. Never leave to recite this supplication after every (prescribed) prayer: "O Allah, help me in remembering You, in giving You thanks, and worshipping You well.". (sunnah.com)
A man was with the Prophet (ﷺ) when another man passed by and the former said: "O Messenger of Allah! I love this man (for Allah's sake)". Messenger of Allah (ﷺ) asked, "Have you informed him?" He said, "No". Messenger of Allah (ﷺ) then said, "Tell him (that you love him)". So he went up to the man and said to him, "I love you for the sake of Allah;" and the other replied, "May Allah, for Whose sake you love me, love you." [Abu Dawud]. (sunnah.com)