The password "foo" may encrypt to the hash "12345". If an attacker were to discover that the hash is "12345", they would look for a password that hashes to "12345", which could, hypothetically, be the password "bar". They don't know the original password "foo", they've simply discovered an alternative, which happens to match the algorithm enough to unlock access.

In general, rainbow tables are used for identifying and attacking common passwords, but that doesn't mean that the algorithm is insecure.

Insecure algorithms can be attacked through collisions, which don't necessarily give you the original password, they just provide an alternative password which is accepted by the algorithm. The distinction matters when it comes to password reuse, because if Site A uses MD5, but Site B uses sha512, finding a collision that grants access on Site A doesn't necessarily give you a password that will grant access on Site B.