This is the 353rd most frequent German word.
hälfte
"Half."
Here, 'Hälfte' is used as a noun meaning 'half,' representing a part of the whole (the cake).
Ich habe die Hälfte des Kuchens gegessen.
I ate half of the cake.
In this sentence, 'Hälfte' again refers to one of two equal parts of something, and 'andere Hälfte' specifies 'the other half.'
Kannst du mir bitte die andere Hälfte geben?
Can you please give me the other half?
Here, 'Hälfte' is used idiomatically to indicate a midpoint, specifically halfway along a route.