The context parameter can be omitted. But if you need it, it has to be the second parameter.

So both of these are fine:

exports.handler = async (event, context) => {};

and without context:

exports.handler = async (event) => {};

You can read more about NodeJS handlers and context in the official AWS documentation:

1. AWS Lambda function handler in Node.js
2. AWS Lambda context object in Node.js

Event represents the event or trigger that caused the invocation of the lambda. For example, if your lambda is triggered by an upload to S3 this will contain information about the object being uploaded for example:

    {
      "Records": [
        {
          "eventVersion": "2.0",
          "eventTime": "1970-01-01T00:00:00.000Z",
          "requestParameters": {
            "sourceIPAddress": "127.0.0.1"
          },
          "s3": {
            "configurationId": "testConfigRule",
            "object": {
              "eTag": "0123456789abcdef0123456789abcdef",
              "sequencer": "0A1B2C3D4E5F678901",
              "key": "HappyFace.jpg",
              "size": 1024
            },
            "bucket": {
              "arn": bucketarn,
              "name": "sourcebucket",
              "ownerIdentity": {
                "principalId": "EXAMPLE"
              }
            },
            "s3SchemaVersion": "1.0"
          },
          "responseElements": {
            "x-amz-id-2": "EXAMPLE123/5678abcdefghijklambdaisawesome/mnopqrstuvwxyzABCDEFGH",
            "x-amz-request-id": "EXAMPLE123456789"
          },
          "awsRegion": "us-east-1",
          "eventName": "ObjectCreated:Put",
          "userIdentity": {
            "principalId": "EXAMPLE"
          },
          "eventSource": "aws:s3"
        }
      ]
    }

Here is detailed information about events, with an example.

Context Provides information about the invocation, function, and execution environment of your lambda. So you can use this to check the memory allocation or to retrieve the number of milliseconds left before the execution times out. Here is detailed documentation about context, with an example.

From v4.0 you need to use getCurrentInvoke as described in @cooow's answer.

Prior versions supported serverless-express/middleware:

... which exposes the event and context objects. You add it like this:

const awsServerlessExpressMiddleware = require('aws-serverless-express/middleware')
app.use(awsServerlessExpressMiddleware.eventContext())

Once this middleware is configured the event and context objects will be added to the request. You access those objects like so:

var event = req.apiGateway.event;
var context = req.apiGateway.context;