Why convertible notes exist
Convertible notes beat equity as the financing of choice for early stage startups largely because they were faster. While later stage companies can afford the time necessary to negotiate long sets of terms, early stage companies don't have that luxury. Not only are prices for such early stage entities nearly impossible (and therefore time consuming) to determine, time is itself the most limited resource a startup has - it's critical to raise quickly and get back to work. Though equity financings can be standardized up to a point, there's always a huge sticking point for negotiations: price. Rather than try standardizing, convertibles notes simply got rid of price as a term.
While the notes eliminated price, they needed structures to govern what the investment would be worth when a price finally did come into play. Price was replaced with two other mechanisms - a discount rate and a cap. While each of these was a negotiable point, they were each and cumulatively less meaningful than price, because they deferred the core pricing question to the next round of financing. Ideally, that meant shorter negotiations on less significant terms. With a priced financing meant to take place within the year (based on the note's maturity), investors were willing to punt on pricing while founders were willing to roll their risk a bit further down the road and get back to work.
The cap trap
But a funny thing happened on the way to this ideal state - caps became implied prices. It isn't all that surprising that this happened. The best founders know that setting goals based on real numbers is critical to sustained growth. They're also incredibly competitive. By removing real prices from fundraising, the convertible note nullified a part of the fundraising game that was important to the egos of founders (and investors). Without a number on which to hang their success, startups lost a public way to "prove" how good they were. At that point, the cap became an obvious choice for an approximation of price: It was a hard number, it could/should reflect something about the note holder's expectations of the price at which the company would next raise money, and it is typically not that well understood.
This introduced several unintended problems. The most extreme of these issues was the advent of the "uncapped" note. To some founders, this was the holy grail. In a very naive sense, this implied an infinite valuation - companies were so hot that investors were saying they'd accept any price at some point in the future just to get in. Practically speaking, this scenario - paired with not having a discount - creates a misalignment of incentives between the investor and the startup. Rather than trying to help the startup move as fast and far as possible prior to the next round of financing, investors are actually incentivized to get as low a price on the first equity as possible so that they are able to convert in at a reasonable price. Conversely, the startup wants to move as fast as possible - as all startups should - and give up as little as the company as possible. While that tension always exists on some level, the dynamic is particularly extreme in these cases.
The second problem came from startups who raised too little money with too high a cap. Convertible notes are debt. They accrue interest and have maturity dates. As a result, it tends to be a bad idea to raise too much money through them. While investors rarely call the notes, the accrued interest can become a significant dilutive factor. But, since founders decided that high caps = good caps, startups would do crazy things like raise $1mm on a $20mm cap with one year maturity. The hurdles set for a company in that scenario were almost unimaginable - and contradictory! Inside of a year, that company would have to grow to a point where raising money at above a $20mm valuation was not just possible, but likely. Otherwise, again because of the common misperception that cap = price, they'd have to raise a "down round". However, if by some miracle they raised above the cap, the investors would get the same % they initially agreed to, but would also get higher liquidation preference.
Ironically, while convertible notes were initially designed to allow good companies to raise money quickly and get back to work, the best companies are precisely the ones that most frequently fell into these cap traps.
Being smarter when raising money
Recently, Y Combinator released a new financing instrument, called the safe, designed to eliminate parts of these problems. By removing interest and maturity dates, the safe makes it easier for companies to raise larger amounts than on notes while avoiding putting themselves in impossible situations. However, the ultimate responsibility for restraining the temptation to raise at ever higher caps rests with founders. Understanding how and why convertible notes and safe exist is the first step. That's easy, it's just reading. The second step is much harder, but equally worth it - founders need to overcome their egos. That might be impossible, but it's well worth the effort.
 Notes also have elements of debt: interest rates and maturity.
 I've had conversations with both founders and investors in which it has been apparent that this is one of several terms that are commonly misconstrued. Those misunderstandings lead to different actors using caps as placeholders for different things, which complicates the picture.
 I'm being extreme, but have heard of crazier.
 David Hornik explores this more in his post Just Say No To Capped Notes. He rightly points out that the capped note is an at times awkward compromise, but I disagree that the resolution should be all uncapped notes or all equity financings.