There is a mental block at work when we read of these old covenant priests and their sacrifices over and over again in the book of Hebrews. That is always the danger of written repetition. What the writer intends as emphasizing the important can be read by readers as a boring lack of new thought.
This world of priests and animals and sacrifices is too far removed from us to feel real. The whole account feels dark and violent and religious only in a superstitious sense. And when we try to bring our brains to feel the situation these accounts picture we have to overcome a time/culture gap that feels as wide as an ocean.
Try hard today - work with me - to bring just the first sentence of our text into a living experience - Hebrews 10:11 - "And every priest stands daily at his service, offering repeatedly the same sacrifices, which can never take away sins."
Relate to that man or woman bringing that animal to the priest for sacrifice. It's morning. The sun is just coming up and it's still chilly outside. You wake up and remember the first thing you need to do is collect that lamb or goat. You have to do this because if there's one thing you remember about yourself it's your own sinfulness.