Executing means that the node will do its action and execute other connected nodes. Nodes can be executed by connecting link to the Execute input, or by toggling Also Execute when pushing values.
Some nodes have the On Start property. When this is enabled, the logic will get executed automatically when the game starts, or when the node is spawned into the world. To quickly identify which nodes are executing on start, a red play button appears on the node. This is triangle is always visible on nodes that are executed on start.
On Start is usually used for initializing the game, for example when you need to load values or spawn objects in the world.
You can also execute logic with a Trigger. These can be, for example, a Button that the player can press, or a collision between two objects.
The most basic example would be to make the HypeHype cube jump at the press of a button: