I will try but its not my strongest subject. This is how i understand things;
Serial is where 1 bit is sent at a time over a form of media (i.e. telephone). There are two types which is Synchronous and Asynchronous. Synchronous is where both ends synchronise the communications using some sort of clocking mechansim. Asynchronous has no syncronisation and send start/stop bits (i think).
SLIP is old and rarly used in todays Point-to-Point links. Its used for the Layer 2 (Data-Link Layer) communications over the serial connections. PPP is the better choice now as it has much more functionality within it, utilising the Link Control Protocol and the Network Control Protocol LCP/NCP. These options allow for things such as multilinking several serial links together to increase throughput, header compression, callback and others.
SLIP/PPP is used to encapsulate IP (Layer 3) traffic into a medium for transpotation over the the Point-to-Point connection. Its used in things such as Dial-Up, ISDN, Serial-Links, and more.
As Smurf says, SLIP is a simple and primitive way of obtaining an IP connection across a serial link. One place you still might see it is on older networking kit where, if all else fails, you can reflash the operating software through the serial management port using a simple SLIP application on your PC. An example, should you want it, is the 3Com Superstack hub series, most of them support it. However you'd only use it as a last resort recovery mechanism after you managed to mess up the device's firmware so much that you can't resurrect it over the LAN