A WAN address is sometimes referred to as the public, or outside, address and the LAN as the private, or inside address.
The WAN IP they refer to is the address provided by your ISP (i.e. Comcast, Time Warner, Cox, etc.). If you're directly connected to your modem, it is likely providing NAT (Network Address Translation) to connected clients and assigning them a private LAN (Local Area Network) IP in the range of 192.168.x.x, 10.x.x.x, or 172.16.x.x. If you have a wireless router with clients connected to that device both wired and wireless, then it will assign IP's in the ranges I mentioned and provide NAT.
For this discussion, NAT is translating your LAN address, for example, 192.168.10.1 to the WAN address 78.87.169.88. The destination never sees your LAN address, only that to get back to the source (your computer), they need to route to your WAN address. From that point, your modem and/or router does the rest.
Since your thread title mentioned LogMeIn, you don't have to worry about WAN IP's. You run the client on your local computer that is connected to LogMeIn servers -- reporting its availability to their servers when it is powered on. When you try to connect to the your computer from someplace else using a web browser or LogMeIn Ignition, the LogMeIn servers know how to get to the destination, i.e. your computer.
The LogMeIn servers are really just acting as a proxy to route traffic between the client (you remotely reaching your computer) and host (your computer).