Compilation, review, and audit are three increasing levels of assurance a CPA can provide on a company's financial statements, from simply organizing the numbers as presented to actually verifying them against outside evidence.
A compilation is the lightest level: the CPA organizes the company's own numbers into proper financial statement format without testing or verifying any of it. A review goes further, applying analytical procedures and inquiries to provide limited assurance that nothing looks materially wrong, without the deep testing of a full audit. An audit is the highest level, involving independent verification of balances, transactions, and internal controls, and it's what most lenders and later-stage investors ultimately require.
Which level a company needs depends on who's asking and why. An early-stage company usually doesn't need a full audit, but one nearing a large financing round, a loan covenant, or an eventual IPO should expect to need one eventually, and building toward audit-ready books well before it's actually required avoids a scramble later.
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