What is the account and contact relationship in salesforce?
I checked the 'Account Name' field in the Contact object. It appeared as a Lookup(Account). But when I deleted that account, contact also got deleted which tells me it is a master-detail relation. Can anyone explain to me the proper way to explain the relationship between account and contact?
There are four different kinds of account and contact relationships in salesforce platform.
But I like to categorise them in a slightly different way than the help pages:
- Lookup
- Master-Detail
- Hierarchy
- Standard relationships
There are lots of help topics and articles on Lookup and Master-Detail, such as the relationship overview and the relationship considerations topics in help. I don't like including Many-to-Many in this kind of discussion because, for all intents and purposes M:M is just an implementation of two M-D relationships (by strict reading of the docs), or possibly two lookup relationships or a mix of the two.
To dispense quickly with hierarchy relationships, these are a special lookup self-join relationship on the User object. Read up on those on your own. 
So let me talk about my own invented fourth category.
Standard Relationships
If we (salesforce.com) provide you with a relationship between two objects, that is a standard relationship. Not lookup, not master-detail. Why do I bother providing this fourth category? Because it is the easiest way to stop people trying to categorise them as either lookup or master-detail when they often share characteristics of both. When you approach working with any standard relationship the question you really need to answer is, "how does this standard relationship behave." Frequently standard relationships have characteristics that you just can't do with a custom relationship. Ever tried to make a custom relationship polymorphic? Go ahead...give it a try. You will fail. But there are many examples of polymorphic standard relationships.
I like to categorise these in their own separate place independent of lookup/master-detail. In fact, anything standard follows the same rule: it behaves exactly the way that salesforce.com wants it to behave to fit the particular purpose of that standard thing.
In my opinion, the Account-Contact relationship is a perfect justification for this fourth category: it is a little like lookup, a little like Master-Detail, but fundamentally behaves the way it does because we decided it should. That might not be the "proper" way, as you ask, but it is the one that makes the most sense to me.