Accredited investor is a definition in federal securities rules that decides who a sponsor can sell a private offering to. For individuals the commonly used tests are an income test, measured over the last two years with a reasonable expectation of the same this year, and a net worth test measured excluding the value of your primary residence. There are also routes based on certain professional licenses. The exact thresholds and categories get updated, so confirm the current definition with a securities attorney or CPA before you sign anything, because the certification is your statement, not the sponsor's.
On your specific confusion: the net worth test is a net worth test, so equity in investment property counts as an asset the same as anything else, and there's no requirement that assets be liquid. Your primary residence gets carved out, and mortgage debt on it is treated specially, which is exactly the part people get wrong when they do this on a napkin. Retirement accounts are assets you own.
What you'll be asked for depends on how the offering is structured. Some private offerings only permit self-certification through a questionnaire and rely on a pre-existing relationship with the sponsor. Others are generally advertised, and in those the sponsor is required to take reasonable steps to verify your status, which in practice means tax returns, brokerage statements, or a letter from your CPA or attorney. If a sponsor is running ads and still only asking you to check a box, that's a real signal about their compliance work generally, and compliance sloppiness rarely stops at one document.
