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Oh, well, "functional analysis" can hardly be an intuitive topic, but it talks about topological (normed) spaces and operators defined in them. There might be some simple examples, though, which might shed you a light when you walk in dark. There are a few fundamental theorems in functional analysis and the quality, in my opinion, of the books are more or less determined by if the books are helpful for you to understand those theorems. Those theorems are "Hahn - Banach theorem", "Open - Mapping Theorem" and "Closed - Graph Theroem".
Here are a couple of books:
Functional Analysis, by Kosaku Yosida. This book is the favorite of math students. It has a few chapters telling about the distributions defined as linear continuous functional over the space of smooth functions.
Functional Analysis, by Walter Rudin. This book is widely used by both math students and the students in other specialities. It has a lot of exercises and examples.
I am pretty sure I saw the electronic versions being circulated around.
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