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#1) The original picture straight off the camera:
3,456 x 2,304 and 3.61MB
Way too big for displaying on the web or for emailing!

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#2) Taking the original image and reducing in scale to a size appropriate for the target audience, and then compressing at 50% quality level to further reduce bytes resulted in a picture
540 x 360 and 54K.

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#3) Taking the original image and cropping away a good portion of it, then reducing the remaining image in scale and compressing at 60% quality resulted in a picture
423 x 370 and 31K.

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#4) Taking the original image and cropping away everything but the subject, then compressing at 70% quality level resulted in a picture that is
336 x 310 and 32K.
This is called a 100% crop because the image is never enlarged or reduced in size; you're just cutting away everything but the choosen subject which remains actual size.

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1) You're making much better use of available screen real estate. The image is smaller, yet the subject is bigger! In #2, my Grackle here is just a dark shape on a branch, but with a 100% crop, I can show him off in detail.
2) Byte size is much less, meaning faster load time.
3) Quality is better. By cropping away all those extra pixels, you're already lowering byte size, therefore you don't need to compress the quality as much. In #2, I went down to 50% in quality but the image is is still 22K larger than #4 at 70% quality.

1) Because the subject is larger and of higher quality, detail is much more apparent. So any flaw in the picture is much more noticable. If the subject is a bit out of focus or if there's noise or if there's a speck from dirt on the lens, you're going to see it. If you're concerned about showing off a technically perfect picture and your picture isn't technically perfect, then this isn't for you.
2) If the composition of the photo is important, then cropping is obviously going to ruin that.