万が一 means "in the unlikely event that": literally "one in ten thousand", a possibility remote but serious enough to plan for. It opens a condition, so the clause it starts ends in , , or .
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In the unlikely event of a fire, use this emergency exit.
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If by any chance it rains, the game will be called off.
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Even if you do fail the exam, you can just try again.
As a noun: 万が一の場合, 万が一に備えて
万が一 can stand as a noun for the unlikely event itself. It takes の before another noun, and and mean "just in case".
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Let's keep some emergency food in case the worst happens.
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I made a copy of my passport just in case.
is a soft way of naming an accident or a death without saying it.
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If anything should happen, call this number.
万が一 or もし
is a plain "if". 万が一 adds that the thing is very unlikely, and that it would be bad if it happened, so it suits warnings, emergencies and precautions.
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If you have time, please help.
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If by some chance I'm not there in time, please start without me.
(まんいち) is a shorter form of the same word, more usual in writing.
Lingaku