rundherum
around
In a circle around something; on all sides.
Um den See führt ein Weg rundherum.
There is a path all the way around the lake.

around / completely
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around
In a circle around something; on all sides.
Um den See führt ein Weg rundherum.
There is a path all the way around the lake.

'Rundherum' is made up of 'rund' (round) and 'herum' (around). It reinforces the idea that something forms a complete circle or is considered from all sides.
Wir sind einmal rundherum um das Schloss gelaufen.
We walked once all the way around the castle.
The spatial meaning ('in a circle') is often recognized by verbs of movement or position, such as 'gehen' (to go/walk), 'fahren' (to drive/go), or 'stehen' (to stand). The figurative meaning ('completely') usually appears with adjectives, such as 'zufrieden' (satisfied) or 'glücklich' (happy), or nouns that describe an event.
Rundherum standen hohe Bäume.
Tall trees stood all around.
In the meaning 'völlig' (completely), 'rundherum' is often combined with positive adjectives: 'rundherum zufrieden' (completely satisfied), 'rundherum glücklich' (completely happy), or in the phrase 'ein rundherum gelungener Tag' (a completely successful day).
Nach dem Urlaub fühlte sie sich rundherum erholt.
After the vacation, she felt completely rested.
whole / quite
'ganz' and 'rundherum' can both express that something is complete. 'ganz' is more general and, depending on the sentence, means 'completely', 'very', or 'the whole thing'. 'rundherum' often has a spatial meaning: something is surrounded or covered on all sides. It can also mean 'completely' in a figurative sense, but then it often sounds a bit more image-based. Learners may confuse the words because both can sometimes mean 'complete'. When you really mean all sides of something, 'rundherum' is more precise; when you are talking about completeness in general, 'ganz' is more natural.

Nach dem Regen ist der Gartenzaun rundherum nass.
After the rain, the garden fence is wet all the way around.
Der Gast bleibt, bis das ganze Essen fertig ist.
The guest stays until the whole meal is ready.