There are fundamentally two kinds of attacks, preimage which splits into two:
In a first-preimage attack, you know a hash value but not the message that created it, and you want to discover any message with the known hash value; in the second-preimage attack, you have a message and you want to find a second message that has the same hash. Attacks that can find one type of preimage can often find the other as well. A weak algorithm allows this to be done in less than 2^(hash length) attempts.
And then there is collision: two messages which produce the same hash. A weak algorithm allows this to be done in less than 2^(half of hash length) attempts.
Weak means that a mathematical flaw has been discovered that makes it inherently insecure, or that it is so simple that modern computer technology makes it possible to use “brute force” to crack. Strong means that it's not either.
