Partition divides large amount of data into multiple slices based on value of a table column(s).
Assume that you are storing information of people in entire world spread across 196+ countries spanning around 500 crores of entries. If you want to query people from a particular country (Vatican city), in absence of partitioning, you have to scan all 500 crores of entries even to fetch thousand entries of a country. If you partition the table based on country, you can fine tune querying process by just checking the data for only one country partition. Hive partition creates a separate directory for a column(s) value.
Bucketing decomposes data into more manageable or equal parts.
With partitioning, there is a possibility that you can create multiple small partitions based on column values. If you go for bucketing, you are restricting number of buckets to store the data. This number is defined during table creation scripts.
Hope this helps.