Modems
Modem, an acronym for Modulator Demodulator simply converts the analog data from internet cables and supplies it to the PC in the digital form. Separate modems are now available for Dial-Up and DSL networks. The DSL Modem delivers the network to the PC via the Ethernet/USB port unlike Dial-Up. The other popular type of modems is the wireless modem, which provide a wireless interface between the modem and the ISP network. But this interface tends to be comparable to dial-up hugely attributed to the distance of the nearest ISP network transmitter. But recent years have seen a marked increase in the provided speed.
Splitter
A simple component becoming obsolete with the dial-up networks, which is used to split the PSTN line into two channels, Internet and Voice.
Routers
You can connect to your modem to gain internet access, but what do you do if you have a guest intending to access internet or simply more than one computer needing internet access simultaneously? The Router comes to the rescue. Routers manage the information transmitted between your LAN and the internet. As the name suggest they can handle/route the requests from multiple computers by splitting the internet signal. There is more to than meets the eye!
> Routers can connect together multiple LANs or even WANs(Wide Area Networks) thus acting as a Traffic Cop.
> The router is provided with a IP address by the ISP called the Public IP Address. The router then uses the DHCP (Dynamic Host Configuration Protocol) server to dynamically assign a Private IP Address to each of the computer that connects to it. A NAT(Network Address Translation) is in place to masquerade the IP address of the source comnputer, thus enabling the router to pose the request to have sourced from the router's IP instead, thus making the actual computers virtually invisible to the internet world.
> This NAT can act as a firewall, protecting the computer from deadly viruses or trojans sourced within the internet. However the firewall does not prevent the outflow of infections.
Wireless Access Points
With the advent of wireless technology, came the convenience of wireless networks. Wireless hotspots started emerging in cafes, public libraries and airports . All these employ something called as WAP(Wireless Access Points). Just like how self explanatory the rest of the networking jargons are so is this. So it is just a portal for wireless client to connect to a LAN or similar to a cellular tower emitting wireless signals. Point to note is that the WAP does not have the inbuilt ability to manage multiple connections unless connected to a router or a modem with inbuilt router, without which it is a dumb wireless signal transmitter supporting only one connection at a time.
Wireless Routers
When the WAP just adds a wireless interface to the wired router, why not come up with a router with inbuilt wireless interface is a question to which the Wireless Router is the answer. Presently these are gaining popularity with the ease of usage and configuration. However WAPs are still employed in public areas unlike at home where it is more of a luxury than a necessity.
I picked up a good illustration from the Microsoft website that simplifies all that I rambled until now :)