At its heart, King Lear is about the relationships between parents and children. Lear believes that vocal expressions of love prove that his children care for him. He fails to understand that an honest child is more sincere, and fails to recognize that a child can disagree with a parent but still love him. The play - through both Lear and the Earl of Gloucester - demonstrates how easily a parent can be manipulated, and how dangerously that parent can misunderstand and take for granted a loving child.
To briefly summarize the story - King Lear asks his three daughters to speak their love to him, so he can decide who most deserves his inheritance. When his youngest is honest with him about her complaints, he disinherits her, and plans to move in with the older two. They quickly weaken him and destroy his belief in their love. He wanders into a storm, upset and disillusioned. Cordelia arrives with the French army to restore her father's kingdom. The two make up, but are soon taken captive by Edmund, who is seeking power. Cordelia dies, sending Lear into torrents of grief and killing him. Goneril and Regan fight and both die. Edgar, the rightful heir to Gloucester, is left to restore the kingdom.