LANs and WANs sound technical and complex, like many terms in the IT arena. However, unlike many networking acronyms, they are fairly straight forward.
LAN stands for Local Area Network and refers to a group of devices (computers, tablets, printers etc) connected together, usually within the same building. Connecting all the devices is typically done either via Ethernet cables, with network switches and/or WiFi access points.
LANs are very fast and can transmit data at speeds up 1000mbps aka 1Gb or 1 Gigabit
WAN stands for Wide Area Network and refers to the method of connecting two or more LANs together. A WAN will cover a broader area like a city or country and there are several connection mechanisms available. The internet is a public WAN. The most common way to create a WAN is by using internet connections like ADSL/FTTC broadband or a dedicated fibre ethernet circuit. However, you can create a WAN using microwave links or high powered outdoor WiFi devices, although these methods would only cover shorter distances. When using a public WAN (e.g. the Internet) to move data between two LAN's, you will want to keep the data safe and secure. You can do this by creating a VPN (Virtual Private Network) between the routers on each site.
WANs are slower than LANs and in the SME arena the speed is generally dictated by availability of fibre broadband in the geographic location of each LAN.
The demarcation point, for the data on the LAN and the data on the WAN, is the router/firewall.