To forsake duties means to give up doing something that you should do, or said that you would do.
There are three types of duties: Duties towards:
- Allah
- Muslims
- Mankind (including yourself)
An example of forsaking a duty towards Allah is not offering your prayers. This is HARAAM, and those people will not receive Allah's favour. The duties towards Allah are also duties to yourself, since everything that Allah has commanded us to do it for our own benefit
An example of forsaking a duty towards Muslims is not burying a dead body. When a Muslim dies, it is WAJIB to give the body Ghusl and make sure that it has been buried according to Islam. If this is not done, then everyone who knew about the death will get Gunah.
An example of forsaking a duty towards mankind is to cause harm to something that others need or use. Imagine you have a farm by the riverside, and you deposit fertiliser and other chemicals into it. If further downstream, people rely on that water for drinking, then it is your duty to ensure that you do not pollute the rives. It does not matter whether those people are Muslims or not, friends or enemies.
Islam is a religion for the whole world, and has rights for all things. Every creature, be it plant, animal of person has rights set by Islam, and we should learn to respect and obey them.