there are many reasons for using Distributed Systems:
After joining various systems (nodes) with a network, user of one system (node) can use resources available at different system (node).
- user of node A can use laser printer connected to node B,
- user of node B can use a file stored at node A,
- possibly more.
'Load Sharing' for Speed of Computations.
if a certain computation can be split into a collection of partial computations that can be simultaneously computed, then a distributed system can allow assigning these partial computations to certain systems (nodes), can also allow for their concurrent computations.
there's also possibility of moving a certain 'computing task' from 'overworked node' to 'another node' when/if neccessary.
if/when one of work-stations (nodes) fails, breaks, then other work-stations (nodes) can still continue their work. missing task(s) can be assigned to one or more of remaining work-stations (nodes).
there's possibility of work-stations (nodes) communicating with each other.
either software communicates for a certain task completion, or work-stations' (nodes') users can communicate as well.
see also, if You wish or need ... : Parallel & Distributed Systems, Stitie Space.