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.