In the simplest terms, the legislative branch makes the laws and the executive branch enforces them. Let's use the United States as an example. The legislative branch, which is led by Congress (a.k.a. the House of Representatives and the Senate), debates new policy, writes laws, and passes laws. They're the only branch that can introduce new bills to be considered by the Senate and the House.

The executive branch is led by the president. He or she implements the laws that Congress makes and can recommend new laws as well. The president has the power to veto laws passed by Congress and to issue directives, known as executive orders, that manage federal government operations.

The legislative and executive branches are also related in that the House has the power to impeach officials, including the president, as well as the power to approve treaties. Additionally, it's Congress, not the president, that technically holds the power to declare war. Congress also has the power to create spending bills, which may or may not include what the executive branch wants.