Should you start your proposal with an "Understanding" section?

Does the RFP ask for one? If it does, you have to provide one. If it doesn’t, you might want to think twice before you add an “Understanding” section.

Are you making the customer read a patronizing section about stuff they already know about themselves before they get to find out what you’re going to do for them? A better approach may be explaining what you are going to do for them in a way that shows insight and demonstrates your knowledge and understanding (as opposed to claiming it). Nothing should get in the way of the customer discovering what they’ll get if they accept your proposal, because that’s the only thing motivating them to read it.

Instead of describing your understanding, consider doing this instead

But even if they’ve asked you to "describe" your “understanding,” that may not be what they really want. The best way to demonstrate understanding to a customer is usually not by reciting the problem, reciting the customer’s mission, describing their current state, etc. 

Customers often ask for descriptions of things when the real issue is that they want to know whether they can trust you to deliver as promised. They want to know if you have the capability to deliver what they want, so they ask you to describe your capabilities. They want to know if you understand what it is they really want, so they ask you to describe your understanding. It’s not your capabilities or understanding that they really want to know about, it’s whether they’ll get what they want. They want to know if you know where they want to go and what it will take to get there. They want to know if you understand the best way to accomplish that. If you are a complete outsider, you probably won't have the insight they are looking for. So they are giving you a chance to demonstrate your insight. Recitations won't provide that.

If this is the case with your customer, then you should respond by making your understanding part of substantiating that they’ll get what they want. In fact, it’s not your understanding that matters at all, it’s how your understanding translates into the customer getting what they want that matters. Why you do things can matter more than what you do when it shows that you understand how to achieve what they want more than anyone else. 

How do you know what the customer means when they say "understanding"?

The most important consideration is how the particular customer in question will perform their evaluation. Different customers have different cultures, expectations, and decision processes. For example, a customer from an academic culture might have very different expectations from a business customer. B2G and B2B have very different evaluation processes. Etc. The impact of understanding on a commodity product procurement is very different from the impact of understanding on a complex solution procurement.
 
A customer who is used to reading research papers, written studies, engineering change requests, or similar documents might have an expectation that documents should start by stating the problem or your understanding.  But while you should give them what they expect, they still need information to make a procurement decision. A demonstration of understanding can provide that, while a recitation may not. 

Who decides whether your proposal should have an "understanding" section?

Ultimately, the correct approach for a given proposal is not determined by you, me, or anyone other than the customer. The most important part of proposal writing is not the writing itself, it’s discovering the customer’s preferences so you can adapt your offering and presentation to match them. But interpretation can be tricky because customers do things like ask you to describe things when they don’t really want descriptions. Except that sometimes they do. Those tricky customers…