There are two basic answers for this:
You are an audiophile, and like the sound of analog recordings, or you simply like the aesthetics of vinyl records, packaging, and turntables. It can absolutely be both!

But the aesthetics, the physical aspect of it, is pretty key to its appeal. These records are more beautiful and substantial than CDs, which mostly have the look of office supplies, and they're the best way to make purchasing music feel like something.

Vinyl allows you to have a sentimentality about albums — there's a tactile quality, a ritual to pulling a record out of a sleeve and putting it on and focusing your attention on the act of listening for a side at a time. 

Even if you still mainly listen to music on your computer or iPod, it gives you the option of having a more special experience with your favorite albums, and an object you can display in your home.

RPM stands for revolutions per minute, as in how many times the platter will spin completely in a minute. Vinyl records are produced to be played at one of three speeds: 33 1/3 RPM, 45 RPM, and 78 RPM. You will almost never deal with 78 RPM records, so don't worry about that. Most full-size 12-inch records will be 33 1/3 RPM, though some — mainly EP's and maxi-singles — will be at 45 RPM.

The vast majority of 7-inch singles will be 45 RPM, and 10-inch records...well, that's more of a wild card. The RPM of a record will be printed somewhere on the record label, and all you need to do is switch your turntable from 33 1/3 to 45 mode.

Vinyl comes in different sizes mainly based on how much music is contained on the record. A standard 7-inch single is smaller than a full-length album because it contains less music, and is intended to be less expensive. But there's also a limit to how much sound can be crammed onto a side of vinyl of any size before the quality of the audio deteriorates because the grooves are too narrow to contain all of the detail of the sound recording.

This is why many records released as a single CD have to be issued as a double album on vinyl — 12-inch sides typically top out around 22 minutes, but albums designed for CD typically spill over 60 minutes — and why many 7-inch singles feature edits of songs that are normally extended over the five-minute mark. But this limitation can be turned to an advantage in that putting less music on a larger side can improve sound quality, which is part of why many singles designed for DJ use are pressed as 10- and 12-inch records to accommodate extended mixes while allowing for excellent sound quality.

Buying vinyl records today is the only way to purchase music that is likely to give you a return on your investment. You can't resell a digital file, and in most cases, CDs have almost no value on the secondary market.

Vinyl records — new or old — retain a lot of value, and so long as your copy is in decent condition and there's some demand for the title, you can often make a profit if you choose to sell.

You probably shouldn't get into buying vinyl as a way to make money — there are much better and easier ways to do that — but it's definitely nice to know that if you had to, you could sell your collection.

Analog means that there is a continuous signal in which the varying part of the signal is a representation of another time-varying quantity. So, when it comes to sound recordings, the instantaneous voltage of the signal varies continuously with the pressure of the sound waves.

Basically, the groove of a vinyl record is like a drawing of the sound wave in a single continuous line through the entire side. Your turntable essentially reads that and decodes it in real time, which results in the sound you hear from the speakers.

Digital signals are not continuous. They are discrete, which means that they send a series of samples of an audio signal's power at precise intervals. Sound does not naturally break down, so a digital system subdivides it into bits, the smallest possible form of information.

This is binary code, so everything is broken down into one of two directives, which is typically described as 0 and 1. The benefit of binary code is that by breaking down information to its smallest possible form, it can represent virtually anything with only two elements. To imagine this visually, it's like plotting points on graph paper.

This sounds terrible, but the reality is that the end result of an analog or digital signal is exactly the same after it is processed through an amplifier and played through speakers: You hear a continuous sound wave. There is no objective way to analyze the end result to determine whether the source was digital or analog because we cannot actually hear digital code or analog voltage fluctuations.

If your records are clean and dust-free, they will play without a lot of pops and clicks. There are a lot of products on the market for cleaning records, but it's easiest to just buy a record brush and/or a simple record-cleaning kit with a soft towel and a cleaning solution that won't break down plastic.

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You should always store your records in a cool, dry place, and have them standing up vertically.

If you stack them on top of one another, you run a high risk of warping the vinyl. If your records are warped, they will never sound right again, and you can't fix it.

A record warps when it bends or melts out of shape. You can play a mildly warped album and it will just sound a little weird. But if a record is severely warped, like the one below, it's totally unplayable.

Watch out — this kind of extreme warping can happen if your record is hit with direct sunlight for an extended stretch of time.

A lot of new albums and singles are pressed on colored vinyl. Though some audiophiles dislike this and strongly prefer black vinyl because the carbon black added to the plastic used for pressing makes it slightly more durable, it will sound pretty much the same as standard black vinyl and often looks very, very pretty.

If you care about aesthetics, colored vinyl is a major bonus, and you might end up going out of your way to get the colored pressing of new albums since they are often produced in limited amounts.