He'll is the short written form of he will, and sometimes of he shall. You use it when you talk about what a man or boy is going to do, or what you believe will happen: “He'll call later.” The apostrophe shows that letters have been left out. In careful or formal writing, people often put he will back in full. He shall is older and more formal; in today’s speech he'll almost always means he will, not a special “shall” meaning. It is a short form of grammar on the page, not a new vocabulary word.