An Execution is the record of a single run of a Pipeline. It contains all the information about that run - when it was run, who ran it, what data was produced etc.
Nextflow pipeline runs consist of a series of invidual processes, which run in their own self contained environment and have their own inputs and outputs. These are chained together to form the entire pipeline execution. You can see all the processes that executed within an Execution (or watch them running live if the run is ongoing). You can also see all the Data that is produced.
Executions and Data together form a network, with Data nodes feeding into Execution nodes, which themselves produce more Data nodes.