You are given a tree of nodes. Each node has a value. Two types of queries: update a node's value, or ask for the sum of all values in a node's subtree. Brute force: traverse the subtree for every query. That is per query, too slow for and queries.
Euler tour converts this into a range query problem. The range representation means you can use efficient range query structures to answer subtree questions in logarithmic time.
Space complexity is for the data structures used.