Great question. Hope the below helps:

Transparent Mode: In this mode, the ASA will filter traffic without requiring L3 on the ASA. This means that in your config you will not put IPs on the interfaces to be used for traffic filtering. Thus, filtering is transparent to the traffic as the traffic isn't directly routed to the firewall. Think of it like you have a server plugged into a switch. In transparent mode, you place the ASA between the server and the switch and no configuration change is required to the server. In routed mode, you place the ASA in the same physical location between the server and switch, but have to change the server to use the ASA as a default gateway.

Single Mode: Default mode of an ASA. The ASA acts as a single firewall and all interfaces are provisioned to be managed through a single firewall configuration.

Multiple Context Mode: The ASA is split into multiple virtual configurations. With the ASA now virtualized, you provision the physical interfaces on the ASA to the virtual firewall configured. Each context has it's own configuration seperate from the rest of the firewall. Multi-context is meant for enterprises to invest in a single piece of hardware and scale it for use as multiple security devices.

Hope this helps. Let me know if you have anymore questions!

-Mike

http://cs-mars.blogspot.com