A Bash alias is often used for commands with a long option list that you use regularly and want to save yourself some time typing or reading the man file each time you wish to run the command.
A good example of this (for me) would be nmap, I often run nmap scans against boxes, and I have memorised the options I use, to save myself some time I might create the following bash alias:
Bash Alias Example
I would normally run a scan using:
So I could create the following Bash alias:
Now I can use the command:
The above will run a scan on a host and it will execute nmap -sS -sV -P0.
Aliases are limited to a simple textual shortcut, if you need more power use a bash function instead.