What determines the clearness of a photo when increasing the size?

I've been taking photos with my iPhone 4S and yes the pictures are great but I recently found out when I find a picture I decide I would like to blow up and print ( larger than a 8 by 10) it comes out blurry. Does the higher the megapixel Make it able to be enlarged? I'm now looking into a dslr canon.

Use 200 pixels per inch, per side as a guide for printing crisp photos.

For example, if you want a 4" x 6" picture then (4x200)x(6X200) = (800X1200) = 960, 000 or approximately 1 Megapixel.

To print a 5x7 you need (5x200)x(7x200) = 1.4 Megapixel

To print a 8x10 you need (8x200)x (10x200) = 3.2 Megapixel

And to print 11x14 you need 6.2 Megapixels.

Sharpness and the megapixel count are the two most important factors.

In landscape mode the iPhone's camera outputs pictures that are 3264 x 2448. At 200 dpi, or pixels per inch, so you should be able to print pictures at 16x12 without stretching the photo.

However, the iPhone 4S camera lacks sharpness, so that is why your pictures look soft.
If you're serious about photography and making large prints a DSLR would be a good option. The Canon Rebel series should be good for you.

The size and resolution of the original image file.

You can view your image at 100% on your computer monitor and if you open the Image Size tool to see what the native size of your image is.

Blur is caused by camera movement during the exposure. Out of focus is just that. The focus point is somewhere other than the subject and Pixelation is caused be attempting to enlarge a print beyond its 100% size. Which exactly is it your are seeing on your 8x10 inch prints?

Look at the Nikon D3200 or Canon T3i/600D entry level dSLR cameras. Visit a proper camera shop to see which one fits your hands the best and is easiest to use.

More pixels is what determines IF the image is clear to begin with. Taken with an IPhone, it's probably focused ok, but you're very, very likely to have motion blur. Any kind of blur is going to be magnified when it's enlarged, regardless of how many pixels it is.