Does Allah forgive sins against other people?

Yes, Allah forgives when you repent, but when you have wronged another person you also have to put it right with that person. Repentance alone does not cancel someone else's right. You need to return what you took, apologise or ask for forgiveness. If it is not settled in this life, it will be settled on the Day of Judgment.

Two kinds of rights

Rights of Allah: prayer, fasting and other duties. When you fail, sincere repentance is enough, and Allah may forgive.
Rights of people: money, reputation, safety and feelings. Allah can forgive your disobedience in harming someone, but the person's own claim remains until it is met or they forgive you.

Many sins involve both. Stealing, for example, is a sin against Allah and a harm to the owner. For the steps of repentance, see What are the conditions of tawbah?

What the Prophet ﷺ said

The Prophet ﷺ taught that whoever has wronged another person in regard to his reputation or anything else should ask for his forgiveness before the Day of Resurrection, when there will be no money to compensate, and instead good deeds will be taken from the wrongdoer, or the victim's sins loaded on him (Sahih al-Bukhari 2449).

He also asked his Companions who the "bankrupt" person is. He explained that it is someone who comes on the Day of Judgment with prayers, fasting and charity, but has also insulted, slandered, taken wealth or struck others, so his good deeds are given to those he wronged (Sahih Muslim 2581).

How to put it right

Money or property: return it, or its value, or arrange to pay. See Do I have to pay back money I stole before becoming Muslim?
Hurtful words or behaviour: apologise sincerely and ask for forgiveness.
If you cannot find the person or they have died: many scholars say to make dua for them, give charity on their behalf, speak well of them and ask Allah to settle it. For money owed to someone who has died, pay it to their heirs.
If telling them would cause even more harm: for example, confessing a hidden slander that would hurt them, many scholars advise asking Allah's forgiveness and praising the person in the same places where you spoke badly of them.
If the matter is serious or legal: speak to a trusted imam or lawyer first.

If someone wronged you

The Quran says that a harm can be answered in kind, but "whoever pardons and seeks reconciliation, then their reward is with Allah" (Quran 42:40). Forgiving is encouraged, but you are not required to stay close to someone who is unsafe for you. See Do I have to forgive someone who abused me as a Muslim?

Hope remains

If you cannot fix everything, Allah knows your effort. Do what you can, repent sincerely, and trust His mercy. For the wider question of repeating sins, see Will Allah forgive me if I keep committing the same sin?

Key points

Repentance to Allah is not enough alone when you have wronged a person.
Return what you took or ask for the person's forgiveness (Sahih al-Bukhari 2449).
If it is not settled now, good deeds can be transferred on the Day of Judgment (Sahih Muslim 2581).
If the person is gone, make dua and give charity for them.

Tip: Apologise simply: say what you did, say you are sorry, and ask what you can do to put it right. Avoid excuses or blaming the other person.