The Cisco ASA allows security levels to be applied to interfaces, traffic is automatically allowed from a high to low security level interface but not vice versa. It's probably designed for the fairly common use case of a perimeter device between a LAN and the internet. The internet link is set to security level 0 and the inside interface to 100. All LAN traffic is then allowed to flow out. This is shown below:
Prior to version 8.3, access lists (ACLs) had to be applied on an interface and in a direction, e.g.
access-list MYACL extended permit tcp any any eq www
access-group MYACL in interface outside
As soon as an ACL is applied to an interface, it will pass traffic based on the ACL rather than based on security levels. However it gets complicated as traffic coming in another interface that would previously have been allowed is now still allowed, in the example above if you permitted port 80 in from the internet, all outgoing LAN traffic is still allowed.
access-group MYACL in interface outside
Now in version 8.4, Cisco have added the ability to have a single global ACL that applies to all traffic regardless of which interface it uses. This is how most other firewalls work so a welcome change. To do this you create the ACL then apply it with:
access-list MYACL extended permit tcp any any eq www
access-group MYACL global
access-group MYACL global
When a global ACL is applied, it removes all behaviours based on security levels from ALL interfaces. So in the original example, you would need a rule in your global ACL that permits LAN hosts access to the internet. The any/any rule is a good example of what not to do as this now globally means "any address" rather than specific to any particular interface.
Update 2015 It appears that not quite "ALL" security level behaviours are removed, you still need the same-security-level command to allow traffic to flow between interfaces regardless of ACL.