According to the Snowflake documentation, these two system functions are provided by Snowflake to monitor clustering information within a table. A system function is a type of function that allows executing actions or returning information about the system. A clustering key is a feature that allows organizing data across micro-partitions based on one or more columns in the table. Clustering can improve query performance by reducing the number of files to scan.
SYSTEM$CLUSTERING_INFORMATION is a system function that returns clustering information, including average clustering depth, for a table based on one or more columns in the table. The function takes a table name and an optional column name or expression as arguments, and returns a JSON string with the clustering information. The clustering informationincludes the cluster by keys, the total partition count, the total constant partition count, the average overlaps, and the average depth1.
SYSTEM$CLUSTERING_DEPTH is a system function that returns the clustering depth for a table based on one or more columns in the table. The function takes a table name and an optional column name or expression as arguments, and returns an integer value with the clustering depth. The clustering depth is the maximum number of overlapping micro-partitions for any micro-partition in the table. A lower clustering depth indicates a better clustering2.
References:
SYSTEM$CLUSTERING_INFORMATION | Snowflake Documentation
SYSTEM$CLUSTERING_DEPTH | Snowflake Documentation