Getting engaged is a monumental undertaking, in and of itself – letting the world (your family and friends) know that you're engaged can be an even greater hurdle, but it's not an impossible feat. If you've already popped the question, the worst is over.
All that needs to be done now – it's not a necessity, but it can help to strengthen the bond between you and your significant other – is to channel your radiant jubilation; and the best way to accomplish this is to throw an engagement party, which will a) enable you to meet your fiancé’s family, b) declare your commitment, publicly, c) give you an excuse to throw a party with your loved ones.
This isn't considered a “rite of passage”, but it is preferred by an overwhelming majority of couples who want to involve their loved ones in one of the most joyous and profound events of their lives – this will undoubtedly lead to a healthier, more honest and sincere relationship in the long run.

If you have large families, and a lot of people are going to be in attendance, then an informal party would probably be the way to go.
The setting of the party should depend solely on one factor: whether it should be formal or informal. A formal party would involve printing invitations and reply cards, and the budget would generally be a bit more liberal. An informal party would take place in a very laid back, carefree environment (i.e. a backyard party; a barbecue; a cocktail party; etc). If you have large families, and a lot of people are going to be in attendance, then an informal party would probably be the way to go.
This will give everybody a chance to meet each other at their own leisure, and the planning put into the party will be a bit less daunting – an informal party can almost be announced right before the party takes place, and a formal party will require lots of forethought and rigorous work.
Involving Your Fiancé’s Parents
Most likely you've already met your fiancé’s parents in an informal setting so arranging a formal get-together, in order to further “break the ice” should be a walk in the park. How you want to go about doing so is completely up to you.
Traditionally, the bride's parents host the engagement party, but in today's increasingly diversified society, the sky is the limit – the bride or groom can host the party, themselves, or a friend of the bride and groom, or even another family member of each respective family can be designated to host the festivities. This is all completely up to the bride and groom (unless the couple's families come from a dyed-in-the-wool, traditional background, then the parents of the bride will most likely be in charge).