A lightning appliance is a dedicated piece of hardware that runs a Lightning node and Bitcoin wallet. Enabling secure storage, high uptime, and total customizability, appliances are a common way of interacting with the Lightning Network.
There are two models for appliances: paid products and self-hosted nodes.
Connecting to the Lightning Network requires both the ability to run a Lightning Network daemon and interact with the Bitcoin blockchain. On-chain transactions are required for opening and closing channels in the Lightning Network, which necessitates communication between a Lightning Network node and a source of blockchain data. A common advantage of a dedicated lightning appliance is the ability to run a Bitcoin full node on the same hardware as a Lightning Network daemon. Given the storage requirements of running a full node, which entails hosting all historical block data and the current UTXO set, many mobile devices and home computers are unable to do so. Running a local full node removes any dependency on a third party's blockchain data or the risk of using an SPV (Simplified Payment Verification) client.