As per my understanding I think:
I will not get into the details of how HashMap works, but will give an example so we can remember how HashMap works by relating it to reality.
We have Key, Value ,HashCode and bucket.
For sometime, we will relate each of them with the following:
Using Map.get(key) :
Stevie wants to get to his friend's(Josse) house who lives in a villa in a VIP society, let it be JavaLovers Society. Josse's address is his SSN(which is different for everyone). There's an index maintained in which we find out the Society's name based on SSN. This index can be considered to be an algorithm to find out the HashCode.
Using Map.put(key,Value)
This finds a suitable society for this Value by finding the HashCode and then the value is stored.
I hope this helps and this is open for modifications.