From Wikipedia, "A credit score is a numerical expression based on a statistical analysis of a person's credit files, to represent the creditworthiness of that person. A credit score is primarily based on credit report information typically sourced from credit bureaus."
Essentially, your credit score is a number that looks at your past history of credit card usage and loans to determine the likelihood that you will pay back a given debt. Credit Cards with higher limits will want you to have a higher credit score because the credit card company is exposing itself to more risk (you can spend more money on the card). Credit Cards that require lower credit scores (lower "credit needed") will generally have lower limits, or other ways for the credit card company to defend themselves in case of default.