I think we already have been given a simple definition on what accountability is and it says admitting your mistakes instead of blaming others, just to add to that understanding, accountability isn't just all about mistakes and admitting them but also that you as a person can be held responsible for something, meaning that you are true to your words and not a cunning or not straight forward person, so having highlighted what the concept of accountability is we would be looking at why is it important to be accountable?

There was a time in my life when I was always a playful person hence I was never straight forward, always trying to be funny and acting too smart in everything, so that made people most especially my parents not to trust my words, it got to the extent that whenever am lying my mom would always caught me, I wasn't ready to owe up to anything so I never knew what responsibility meant because I was always leaning on others, I kept on going and going in my childishness and foolish thinking I was doing the best for myself but what I never knew at that time was that I wasn't growing.
Accountability itself is a sign that maturity has started for a person and I don't mean the maturity where physical attributes would start growing but mentally, emotionally, psychologically you would mature, accountability brings a sense of responsibility which is like a preparation ground for bigger things, for you not admitting your mistakes is like outsmarting others and painting yourself the saint but in much sense you aren't, we surely are not perfect so let's cut out from putting the blame on others and start owing up to what we have done.
As one of my lecturer would say, if you pass your course you would say you wrote well and passed but when you mistakenly get a bad result or a carryover you would say the lecturer failed me, that's just a picture of putting the blame on others Instead of sitting down to check what made you score this low so as to improve in the next one, when you are known as an accountable person the picture people get is that this person can be trusted, the person is sincere and reliable therefore the trust in that relationship or teamwork can be easily built because you have been tested and trusted.
Accountability is a big key that everyone should be looking at for Incase of first impression or a lasting relationship, so the question lies "can I be accountable" and if you eventually finds the answer please drop it in our comment section 👍.
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We should be accountable for our mistakes not that we should be putting our blames on other people.