An Elasticsearch / Apache Solr index is the equivalent of a SQL table.
An Elasticsearch or Solr server (aka Solr instance, aka Solr engine) can maintain several indexes.
Elasticsearch
Each index contains types, defined with a mapping. The index type mapping is equivalent to a SQL table schema definition.
Apache Solr
Each index is defined by a schema.xml file (it’s not mandatory in Solr 5/6, but recommended in production), and a solrconfig.xml file. The index schema is equivalent to a SQL table schema definition.
An index contains several documents, equivalent to SQL table rows. Each document contains fields, equivalent to SQL table columns.
When an index document is inserted/updated/deleted, we say it is “indexed”.
To retrieve documents from an index, Elasticsearch (json) / Apache Solr (xml, json) provide an http API, with a proprietary syntax.