grundlos
without reason
Without an apparent reason, cause, or justification.
Er hat sich grundlos über eine Kleinigkeit aufgeregt.
He got upset over a little thing for no reason.

groundless
Loading your saved state.
without reason
Without an apparent reason, cause, or justification.
Er hat sich grundlos über eine Kleinigkeit aufgeregt.
He got upset over a little thing for no reason.

The word is built very logically: it consists of 'Grund' (reason, cause) and the ending '-los' (-less), which means 'without'. So 'grundlos' literally means 'ohne Grund' (without reason).
Deine Angst ist völlig grundlos, es wird nichts passieren.
Your fear is completely groundless; nothing is going to happen.
'Grundlos' (without reason) is very often used as an adverb to modify a verb or an entire sentence. It describes that an action happens without any apparent cause.
Sie fing grundlos an zu lachen.
She started laughing for no reason.
Common combinations describe emotional reactions or negative actions. Typical phrases are: 'sich grundlos Sorgen machen' (to worry for no reason), 'grundlos wütend werden' (to get angry for no reason), or 'jemanden grundlos beschuldigen' (to accuse someone without reason).
Mach dir keine grundlosen Sorgen, es ist alles in Ordnung.
Don't worry for no reason; everything is fine.
The literal meaning 'ohne Boden' (without a bottom) is very rare and is used almost only in literary or poetic texts. In normal usage, you should always assume the meaning 'ohne Grund' (without reason).
Er fiel in einen grundlosen Abgrund seiner Träume.
He fell into a bottomless abyss of his dreams.
arbitrary
'willkürlich' and 'grundlos' can both mean that no clear reason is apparent. 'Grundlos' only says that there is no cause or justification. It fits with things like fear, anger, or a dismissal. 'Willkürlich' puts stronger emphasis on the fact that a decision was made randomly, on a whim, or without a rule. It can also sound unfair, especially when someone has power. The words are easy to confuse because both express a missing reason. If you only want to say that there is no reason, use 'grundlos'. If a decision seems unsystematic or unfair, 'willkürlich' fits better.

Nach dem Unterricht war Anna plötzlich grundlos nervös.
After class, Anna suddenly felt nervous for no reason.
Der Lehrer hat die Gruppen nicht erklärt, deshalb fanden viele Schüler die Einteilung willkürlich.
The teacher did not explain the groups, so many students found the division arbitrary.