A layer is simply a group of functionality. The overall infrastructure is divided into layers to create abstraction, simplification and better, more well defined interfaces. The boundaries between the layers are not yet well defined, but as of 2019 one can identify the following 3 layers. There might be more layers created or subdivided in the future as the infrastructure is built out. This is ongoing work.
Layer-1 is the bottom layer providing the basis for everything. This can be seen as a settlement layer. This is implemented as a blockchain with its corresponding currency, e.g. the Bitcoin blockchain is a Layer-1 protocol. Same for Litecoin, etc. This is a layer with slow but very secure transactions that are absolutely permanent. This layer is the best defined layer.
Layer-2 sits on top of Layer-1. The Lightning Network is part of Layer-2. It provides the payment layer. This layer provides fast payment operations that are less permanent. Layer-2, i.e. the Lightning Network, uses the Layer-1 occasionally to settle the accumulated payments permanently. There might be other Layer-2 protocols in the future such as identity management. Lightning is one Layer-2 protocol, but other Layer-2 protocols will be coming.
This layer is less well defined. It contains applications and could be called the application layer. Included in these applications are wallets, custodial services like custodial wallets, exchanges, micro-payment solutions. This layer also includes market-places, web sites and web services that build on top of Layer-2 and make use of Layer-2 APIs.