I'd recommend you break up your question to make it more specific on what exactly you are looking for, but I'll try to add information.
Weaving allows EclipseLink to change the bytecodes of your entities to add provider specific methods etc so that you do not need to introduce a dependency within your model. Each of the terms listed in the doc you found - lazy loading, fetch goups etc - are all performance enhancements that you would need to look up individually. All can be used without weaving, but would require changes to your entity to implement EclipseLink interfaces and methods.
Lazy loading delays fetching a relationship until your application accesses it. getEmployee() in your entity for instance will just return the reference employee attribute - without weaving, the employee must have been fetched already or a null will be returned incorrectly. With weaving, code can be added to the Entity so that it goes to the database to fetch it on demand.
Fetch groups are similar concept that apply to basic mappings instead of relationships, while change tracking is more advanced and allows EclipseLink to be notified when you make a change to the entity rather than having to compare changes with a prebuilt backup on commit. Each will have independent references within the EclipseLink documentation.
