What reason is given for why the woman anointed Christ with "very precious" or costly ointment? What does Mark 14:8 imply that she understood?
She is doing all that she can to express her love to the Savior. That verse specifically calls out that she is anointing Him in preparation for His burial, as though she actually recognizes that there is little time left and that He will be killed.
Why did some of the disciples feel indignant and call her actions a "waste"?
They had not yet come to an understanding of what Christ was preparing them for and that He would not be with them much longer. They had been learning and seeing that it is important to care for the poor and that is where Christ always turned to and they didn't want to feel like they were doing something wrong.
The woman gave of probably her most expensive thing, sacrificing all for the Savior. She gave freely and is an example to us as we should recognize that we can too give all that we have to come closer to our Savior, to show our love and devotion. The things that I could give the Lord now aren't so tangible, because He does not come to my house in the flesh, but others do. We should treat all of our neighbors with graciousness and serve with all of our resources.