If you're using the Company Search endpoint (or any search endpoint) data is supplied in a "paged" format e.g. you'll only get back the first x records. You can then request the next set.
You can specify both how many results and which result in the set to start with using:
This is the number of results requested from CH. Normally defaults to 20 if you don't specify it (this may change). Maximum is 100 I think.
This is the first result in the list to return, starting from zero I believe. Defaults to zero / the first. May be limited e.g. for the searches there may be an upper limit. This may be changed also. If you want lots of data rather than just trying to find a specific result there are several bulk data options (see later).
If you read the following thread you'll get a good overview of how to make this work.
Searches are designed for just that e.g. searching - here's a note about that:
If you want to search through all / large amounts of Companies House data there are various bulk data sets:
Bulk data dumps - may be updated monthly:
List of other data products: https://www.gov.uk/guidance/companies-house-data-products
For officers, you can sign up on this forum - see following thread:
I think they also do some CDs / DVDs with all their data - for a fee.