The depth actually is the maximum number of intermediate certificate issuers, i.e. the number of CA certificates which are max allowed to be followed while verifying the client certificate.
A depth of 0 means that self-signed client certificates are accepted only,
the default depth of 1 means the client certificate can be self-signed or has to be signed by a CA which is directly known to the server (i.e. the CA's certificate is under SSLCACertificatePath), etc.
A depth of 2 means that certificates signed by a (single level of) intermediate CA are accepted i.e. by an intermediate CA, whose CA certificate is signed by a CA directly known to the server.
Our perl test about this directive has some very useful comments and will help you to understand my explanation in a NGINX Context a little bit better.
https://github.com/nginx/nginx-tests/blob/7a9e95fdd30729540ee9650be7f991c330367d5b/ssl_verify_depth.t#L145