보다
boda
Whatever comes before 보다 is the ruler, not the story
The picture Two things stood side by side, with a line drawn at the height of one. Everything the sentence cares about happens above that line. 보다 draws the line and goes past it; 만큼 stops exactly on it.
Where the picture shows up in 보다
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the line drawn at yesterday
어제보다 오늘이 더 추워요.
eo-je-bo-da o-neu-ri deo chu-wo-yo
Today is colder than yesterday.
A line chalked at yesterday's cold, with today's cold standing a hand's width above it.
The standard comes first and the subject second — the opposite order from English 'than'.
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the line drawn at your guess
생각보다 쉬웠어요.
saeng-gak-bo-da swi-wo-sseo-yo
It was easier than I expected.
The job finishing well below the dotted line you had drawn for it in your head.
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the line drawn at me
저보다 형이 키가 커요.
jeo-bo-da hyeong-i ki-ga keo-yo
My older brother is taller than me.
A pencil mark on the wall at the top of your head, and your brother standing with his head above it.
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the line drawn at the bus
지하철이 버스보다 빨라요.
ji-ha-cheo-ri beo-seu-bo-da ppal-la-yo
The subway is faster than the bus.
A notch set at the bus's speed, and the subway's needle sweeping past it.
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the line drawn under everything
무엇보다 건강이 중요해요.
mu-eot-bo-da geon-gang-i jung-yo-hae-yo
Health matters more than anything else.
Money, work and reputation laid flat on the floor, with health set down on top of them.
무엇보다 and 누구보다 end up meaning 'most of all'.
All of it in one picture
Today's cold rises above the line chalked at yesterday's; the job finishes below the dotted line in your head. Your brother's head clears the pencil mark at yours, the subway's needle sweeps past the bus's notch, and health sits on top of everything spread out on the floor. All five do the same thing — draw a line at the first item, then send the second past it. That is why whatever comes before 보다 is only the ruler; the thing you actually want to say is always after it.