OLAP stands for Online Analytical Processing.
It uses database tables (fact and dimension tables) to enable multidimensional viewing, analysis and querying of large amounts of data. E.g. OLAP technology could provide management with fast answers to complex queries on their operational data or enable them to analyze their company's historical data for trends and patterns.
OLTP stands for Online Transaction Processing.
OLTP uses normalized tables to quickly record large amounts of transactions while making sure that these updates of data occur in as few places as possible. Consequently OLTP database are designed for recording the daily operations and transactions of a business. E.g. a timecard system that supports a large production environment must record successfully a large number of updates during critical periods like lunch hour, breaks, startup and close of work.