engross
To be completely focused on something and ignore everything else.
To be engrossed in something means to be so completely absorbed and focused on it that you barely notice anything else around you. When you're engrossed in an exciting book, you might not hear someone calling your name. When a scientist becomes engrossed in examining a specimen under a microscope, hours can pass without them realizing it.
The word suggests a deep, voluntary attention that pulls you in, different from being merely distracted or daydreaming. You choose to read the book or work on the puzzle, but then it captures you so thoroughly that everything else fades away. A video game designer hopes players will become engrossed in the game world. A teacher feels successful when students are so engrossed in a science experiment that they forget about recess.
Being engrossed feels different from multitasking or half-paying attention. When you're truly engrossed, you're giving something your complete mental energy. Your little brother might try to show you his drawing while you're engrossed in building a model rocket, and you honestly don't notice it because your mind is entirely focused on connecting the right pieces. That total focus is what makes engrossed such a useful word for describing those moments when something captures your full attention.