Although photography as an art is largely migrating to digital these days, i'd like to spend a few paragraphs talking about film, because it'll come in useful, i think, in understanding images.
Before digital became as common as it is now, film was the way we got pictures. The way most of us have experienced this in the last quarter century has primarily been via the negative, and to a somewhat lesser extent slides and instant film (Polaroid, and for a span of a few years Kodak). Focusing (if you'll forgive the pun) just on negatives and the concept of making prints from them will help form a foundation from which we can discuss how to compose a strong image, as well, hopefully, explaining some detail about both cropping and why it's not always possible to get good images from particular shots.
Today, in the digital age, it's all about megapixels. This basically equates to resolution- you'll get finer resolution, and thus be able to print larger images without degradation, the more megapixels comprise an image. In the film days, for most users, this would have been 35mm film. At the same time, much professional imaging was done in what is called 'medium format'- itself a blanket term covering a handful of different sizes using common film types (120 and 220).
A 35mm frame measures 24 mm by 36mm. The format itself takes its name from the dimension of the film, including sprocketing, on the shorter of those two sides. The standard print size for this size of film since the 80s was 4 inches by 6 inches (10.16 x 15.25 cm)- which matches the aspect ratio of 2x3 perfectly. Common enlargement sizes are 5x7 and 8x10 (12.7 x 17.8 cm, 20.3 x 25.4 [A5]). Doing just a quick bit of math will show that these two have different aspect ratios completely- the full 35mm frame translates to 8 x 12. Medium format most commonly are 6cm x 4.5cm, 6cm x 6cm, or 6cm x 7cm- significantly larger. The 6 x 4.5 (often simply 645) format shares the exact same aspect ratio as 8x10 prints, but requires 2¼ times less magnification- or, to put it differently, for the same amount of magnification as produces an 8x10 print from a 33mm negative, it's possible to print an 18 x 22.25 image- or either by cropping slightly or using a slightly lower magnification, a standard 16 x 20.
To illustrate, here are two pictures scaled as if they were 35mm and 645 frames respectively:
The 6 x 6 is a square image- so the same image can be printed as a square (albeit these are difficult for which to find either off-the-rack frames or mattes), or can be cropped into either a horizontal or vertical, because both exist in the same frame. Sorry for not having a handy way to represent that in the images above.
In our next piece, we'll discuss a little about how they eye sees images and what makes the difference between an ordinary picture and one which stands out, even of the same subject. Believe it or not, the aspect ratio differences between 8x10 and 8x12 will play a role- and there are a few little tricks which you can use to make ordinary prints better ones just by knowing where to look when you're taking the pictures which relate to that difference.
How's this translate to digital terms? If a 645 image is representationally a 10 megapixel digital file, a 35mm one is about 4.4.