This is the general "to help".
If "weiter" is part of the phrase then it restricts the meaning as I will describe now.
weiter = further, weiterhelfen = to help so. get further or proceed with something.
Example. Someone doesn't understand how to do a math homework. "Kannst du mir weiterhelfen?" means I am stuck with that step and can't proceed, can you help me to get further / to get over my problem?
Or: I don't know where I am / where I have to go and can't find out myself. Can you help me to find my current location / target location on this map?
This is a situation where the one to ask for help cannot get along without help. Perhaps only a small hint or gesture is necessary to help this person.
The words are separated, here "weiter" means "to continue" or "again". Think of "weiterhin".
Example: you helped someone clean the garage but you are not finished. Then after a break or on another day the person asks "kannst du mir weiter helfen?" - can you help me again.
This is a situation where the one to ask for help could work on alone too, but asks for assistance again. As "weiter" is part of the phrase, this implies there already was some help before. If you ask for help the first time you wouldn't say "weiter helfen" because there was nothing that "again" could refer to.
To make it weird in case of the homework example the person could say "danke du hast mir weitergeholfen (1), möchtest du mir weiter (2) bei meiner Hausaufgabe helfen?".
(1) thanks you helped me to understand the step,
(2) do you want to keep helping me with my homework ( ... or should I try on my own)