Very, very roughly: OLTP is for dealing with one row at a time (TP = transaction processing; think “handling a sale”). OLAP is for combining many rows and extracting useful information from them (AP = analytics processing; think “figure out how many sales we had of each type of unit last month”). So for OLAP, you get more emphasis on features like joins, grouping and other analysis.
OLAP databases are column oriented and are optimized for querying large amounts of high dimensional data (E.g. many columns). They're usually used for analytics. They don't support some features that OLTP databases have, like transactions.
OLTP databases are your standard database like MySQL, Postgres, etc.
You use an OLAP database if you want to query billions of rows over many different columns. Obviously they can be used for smaller workloads, but I'm exaggerating to show their strengths.