1) 'Abd needs to have obedience to Allah عزّ وجلّ. This implies that obedience to Allah عزّ وجلّ trumps obedience to anything else. One cannot obey Allah's creation while also obeying Allah عزّ وجلّ. If you obey the creation, you are disobeying Allah عزّ وجلّ in the process and this is shirk, you are no longer an 'Abd.
2) Love (Hubb). We have to love Allah عزّ وجلّ more than anything else. "Those who believe are intense in their love for Allah" (2:165). We love different things, our family, assets, etc. but for believers all of that comes after love of Allah عزّ وجلّ.
3) Tawakkul: We have to trust and rely on our Master. We have embody this attitude: I've accepted myself as a slave, I've accepted Him as the Master, so whatever instructions He gives me I have to trust that they are better for me. Whatever situation He's putting me through, I have to trust Him, in that no matter how hard obeying Him is in that situation, it is better for me. We have to trust that that's true.
4) Sincerity. When we do something, especially an act of 'Ibadah, we have to do it sincerely for the sake of Allah عزّ وجلّ alone. We can't mix other things with Allah عزّ وجلّ. If we're giving sadaqah to the masjid, we can't think yeah it's a good tax writeoff, AND it's good sadaqah. We can't mix those intentions. This sincerity is talked about in the surah Al-Kauthar as well (fa Sallee li rabbik), and in other places as well (6:162). We serve the deen in many capacities. In the beginning it's for Allah عزّ وجلّ, but soon frustration and discontent kicks in and we start thinking we need to be in charge and our ego kicks in. We don't realize it but over time we begin to do it for appreciation. We have to maintain Ikhlas.
5) Terms of slavery. When we get a job, there's a contract with the company. It spells out what each owes other. It's an understanding. For example between a husband and a wife, or parent and child, or government and citizen. Usually these contracts are a result of compromise, and spells out each other's rights. With Allah عزّ وجلّ, these terms are not a result of discussion and compromise. These come from above, we just take them. We are in no position to define or discuss these terms, we can't define what it means to worship or obey Allah عزّ وجلّ. Those definitions are coming from Allah عزّ وجلّ, and that's what makes us a slave.
During Jahiliyah, the kuffar were making tawaf, making sajdah, etc. but the terms of their worship were not as specified by Allah. They came up with it themselves. But Allah عزّ وجلّ says if you do that it's unacceptable. The only way it's acceptable is if it comes from Allah عزّ وجلّ, and the only way it comes to us is through the Messenger. If you worship Allah عزّ وجلّ the way you want, you're not a slave.
'Uboodiyyah is not just worship but also slavery. Two terms, combined in Arabic. So when the Messenger (pbuh) says laa a'budu ma ta'budoon, it doesn't just mean I will not worship, also I will not be enslaved to. Worship is specific acts, but we are always slaves of Allah whether we are doing those acts or not. This is a powerful concept - we are not supposed to live our lives according to how Allah عزّ وجلّ wants us to only in Jumuah or specific times, we are enslaved to Allah عزّ وجلّ in between the prayers too. A lot of the time people worship Allah عزّ وجلّ but don't act like His slave. Partial English definitions contribute to this confusion. 'Ibadah includes both, worship and slavery.
From a lecture by Ustadh Nouman Ali Khan on Surah Al-Kafirun. Watch the lectures here: https://www.islamawareness.net/Quran/VideoLectures/surah109.html