Grasses grow by either stolons (lateral growth), or stolons and rhizomes (underground roots) depending on the turf species. Both stoloniferous and rhizomateous grasses have the ability to encroach surrounding garden beds. This includes stolons growing over edging into the garden, or rhizomes growing under a permanent edge e.g. even concrete kerbing. Maintaining your lawns edges will help to limit encroachment while providing a sharp, tidy, aesthetic lawn.
Edging is largely undertaken using a brushcutter (line trimmer / whipper snipper) or edger where depth control and accuracy can be maintained.